Last update:
Thu Oct 10 08:08:08 MDT 2024
Anonymous Letters to the Editor . . . . . . . . . 1--1
Anonymous Coming Events . . . . . . . . . . . . . 2--3
Gail S. Young Providing a Better Mathematics Education 4--7
June P. Wood First-Year Mathematics --- a Challenging
Variable . . . . . . . . . . . . . . . . 8--13
Fred Toxopeus Summer Developmental Mathematics Program
at Kalamazoo Valley Community College 14--16
Herbert D. Peckham An Integrated Physics-Calculus Course 17--24
Larry C. Elbrink and
Bert K. Waits A Statistical Analysis of
Multiple-Choice Examinations in
Mathematics . . . . . . . . . . . . . . 25--29
Peter A. Lindstrom The Irrationality of Certain Numbers . . 30--31
Carl L. Main Encouraging Mathematical Inquisitiveness 32--36
Anonymous Second-Year Vocational . . . . . . . . . 36--36
R. David Gustafson and
Arnold Wendt Progress Report on Articulation in
Illinois . . . . . . . . . . . . . . . . 37--40
James C. Davis and
Ralph H. Niemann Junior College Cooperative Program in
Colorado . . . . . . . . . . . . . . . . 41--43
Albert E. Hickey The Use of the Computer in Mathematics
Instruction . . . . . . . . . . . . . . 44--54
Jon M. Laible A New Graduate Degree for Mathematics
Teachers in Two-Year Colleges . . . . . 55--58
Anonymous Reviews . . . . . . . . . . . . . . . . 59--59
Carl B. Boyer The History of THE CALCULUS . . . . . . 60--86
Anonymous Statement of the MAA's Role in
\booktitleThe Two-Year College
Mathematics Journal . . . . . . . . . . 87--87
Dwight B. Goodner The CUPM and the Two-Year College . . . 88--90
Anonymous Publishers' Corner . . . . . . . . . . . 91--91
Stanley Schmidt A Curriculum Suggestion for Teaching
College Arithmetic . . . . . . . . . . . 92--95
Anonymous Subscription Information . . . . . . . . 96--96
Anonymous Editorial Board . . . . . . . . . . . . ??
Jon M. Laible and
John W. Milsom and
Robert J. Cohen and
Darrell J. Peterson and
G. Thomas Riggle II and
Ronald Johnston and
C. M. Adams and
Martha C. Jordan and
J. I. Cone Letters to the Editor . . . . . . . . . 1--2
Anonymous Coming Events . . . . . . . . . . . . . 3--4
Olof Hanner Mathematics, A Solitary Game . . . . . . 5--16
Margaret L. Lial Programmed Instruction in Elementary
Algebra: an Experiment . . . . . . . . . 17--21
Aaron Seligman If \ldots Some Suggestions on Presenting
the Connector ``if \ldots then'' . . . . 22--26
Don Ross Remedial or Developmental? Confusion
over Terms . . . . . . . . . . . . . . . 27--31
Carol Kipps Who's Committed? Who's Involved? . . . . 32--35
Larry D. Carter Mini-Math: a Program of Short Courses 36--38
Howard Saar F(1) Rejection Theorem . . . . . . . . . 39--40
Gary G. Bitter Calculus and the Computer: an Evaluation
by Participants . . . . . . . . . . . . 41--49
Ralph Mansfield Two-Year Colleges and Post-Secondary
Education in Western Europe . . . . . . 50--55
Phil Heft and
Charles Ainley Spring Retreat for Community College
Mathematics Teachers in Washington . . . 56--58
Anonymous Reviews . . . . . . . . . . . . . . . . 59--75
Claudia Zaslavsky Mathematics of the Yoruba People and of
Their Neighbors in Southern Nigeria . . 76--99
Lewis H. Coon Gleanings from The Washington, D.C. NCTM
Meeting . . . . . . . . . . . . . . . . 100--103
Anonymous So You Have a Manuscript . . . . . . . . 104--105
John Peterson A Computer-Oriented Multiplication
Algorithm . . . . . . . . . . . . . . . 106--106
H. L. Kung $ \int f(x) e^{ax} \, d x $ . . . . . . 106--107
Anonymous For the mathematics teacher who has
almost everything . . . . . . . . . . . 108--108
Anonymous Editorial Board . . . . . . . . . . . . ??
David T. Switney and
Richard Plagge Letters to the Editor . . . . . . . . . 1--1
Anonymous Coming Events . . . . . . . . . . . . . 2--3
John W. Woll, Jr. One-Sided Surfaces and Orientability . . 5--18
Maurice E. Nott, Jr. New Results of Research Comparing
Programmed and Lecture-Text Instruction 19--22
J. C. Bodenrader Factoring Functions . . . . . . . . . . 23--26
Richard Spangler Lower Columbia College Mathematics
Laboratory . . . . . . . . . . . . . . . 27--31
D. Bushaw Functions Defined by Differential
Equations: a Short Course in
Trigonometry . . . . . . . . . . . . . . 32--35
R. P. Boas, Jr. Calculus as an Experimental Science . . 36--39
Sidney Penner An Interesting Correspondence and Its
Consequences . . . . . . . . . . . . . . 40--44
Elmar Zemgalis On One-Sided Inverses of Matrices . . . 45--48
Mary L. Boas Mathematics for the Undergraduate
Physics Major . . . . . . . . . . . . . 49--52
John B. Davis, Jr. and
T. J. Pignani Two-year College Faculty Participation
in Professional Mathematics . . . . . . 53--57
Paul Lawrisuk Committing Curricular Heresy . . . . . . 58--64
Anonymous Reviews . . . . . . . . . . . . . . . . 65--69
Anonymous The CUPM Consultants Bureau . . . . . . 70--70
Norman F. Lindquist and
Norman F. Lindquist How Are Computers Being Used in Two-Year
Colleges? . . . . . . . . . . . . . . . 71--71
Anonymous Editorial Board . . . . . . . . . . . . ??
Anonymous For the Mathematics Teacher Who Has
ALMOST Everything . . . . . . . . . . . 1--8
Anonymous Coming Events . . . . . . . . . . . . . 9--11
Joseph Hashisaki From the Editor . . . . . . . . . . . . 12--13
Victor Klee Shapes of the Future . . . . . . . . . . 14--27
Richard A. Dean Vectors Point Toward Pisa . . . . . . . 28--39
Donald Perry An Experiment in Teaching Elementary
Algebra . . . . . . . . . . . . . . . . 40--46
Keith J. Roberts and
Leo E. Michels The Crossover Mathematics Program at
Milwaukee Area Technical College . . . . 47--50
William Stark Calculus and the Computer --- CRICISAM 51--54
R. S. Pierce A Strategy for a Class of Games . . . . 55--62
Joseph Hashisaki The MAA and the Mathematics Teacher in
the Two-Year College . . . . . . . . . . 63--68
Charles R. Colvin The Fredonia Plan for Preparing Two-Year
College Teachers . . . . . . . . . . . . 69--73
Anonymous Reviews . . . . . . . . . . . . . . . . 74--86
J. A. Jones Basic Mathematics for Colleges --- the
CUPM Recommendations . . . . . . . . . . 87--92
Jack E. Forbes and
Josephine P. Andree What's New in TYC Mathematics? . . . . . 93--94
William I. Miller $ F(1) $ and $ F(d) $ Rejection Theorems 95--96
Etta Mae Whitton A General Formula for the $N$ th Term of
a Sequence . . . . . . . . . . . . . . . 96--98
Louise S. Grinstein Integration by Undetermined Coefficients 98--101
Anonymous Editorial Board . . . . . . . . . . . . ??
Anonymous Institutional Subscribers . . . . . . . 1--7
Anonymous Coming Events . . . . . . . . . . . . . 8--9
Roy Dobyns A Condition Equivalent to Associativity
for Finite Groups . . . . . . . . . . . 10--13
June P. Wood ``Sample'' Tests for Students . . . . . 14--15
Joanna S. Burris and
Lee Schroeder Developmental Mathematics:
Self-Instruction with Mathematics
Laboratory . . . . . . . . . . . . . . . 16--22
C. A. Long The Quadratic Polynomial and Its Zeros 23--29
D. L. Carleton Using Polyhedrons to Define Maximum
Volumes . . . . . . . . . . . . . . . . 30--32
John M. H. Olmsted and
Carl G. Townsend On the Sum of Two Periodic Functions . . 33--38
Steven L. Kleiman Pythagorean Triples by Geometry . . . . 39--41
Lawrence L. Mitchell Conference Proceedings: Teaching
Mathematics to Occupational and
Developmental Students . . . . . . . . . 42--47
Anonymous Reviews . . . . . . . . . . . . . . . . 48--54
Phillip E. Johnson The Genesis and Development of Set
Theory . . . . . . . . . . . . . . . . . 55--62
Jack E. Forbes and
Lawrence L. Mithchell and
Allen Angel What's New in TYC Mathematics? . . . . . 63--65
Robert L. Page How Steep Is a Hill? . . . . . . . . . . 66--67
Sidney H. L. Kung Talking About Particular Solutions . . . 67--71
William C. Stretton Some Problems of Utmost Gravity . . . . 72--75
Anonymous Subscription Information . . . . . . . . 76--76
Anonymous Editorial Board . . . . . . . . . . . . ??
Anonymous Institutional Subscribers . . . . . . . 1--6
Paul E. Prindle Publisher's Letter . . . . . . . . . . . 7--7
June P. Wood Letters to the Editor . . . . . . . . . 8--8
Jean J. Pedersen Sneaking Up On a Group . . . . . . . . . 9--12
Ivan Niven Which is Larger, $ e^\pi $ or $ \pi^e $
? . . . . . . . . . . . . . . . . . . . 13--15
Karl J. Smith A Program for Keno . . . . . . . . . . . 16--20
R. P. Boas, Jr. Anomalous Cancellation . . . . . . . . . 21--24
William E. Hartnett On the Use of Functions . . . . . . . . 25--28
Karl G. Zahn A Design for Class Testing Mathematics
Textbook Materials . . . . . . . . . . . 29--32
Phillip E. Johnson Academic Qualifications of North
Carolina's Community College Professors 33--36
Peter M. Wilson Do Students Learn From and Like An
Audio-Tutorial Course in Freshman
Mathematics? . . . . . . . . . . . . . . 37--41
Anonymous Reviews . . . . . . . . . . . . . . . . 42--52
Anonymous News and Notes . . . . . . . . . . . . . 53--55
Lester H. Lange A Look at That 1971 MAA Information
Services Survey . . . . . . . . . . . . 56--69
Anonymous Coming Events . . . . . . . . . . . . . 70--71
Norman Schaumberger An Alternate Classroom Proof of the
Familiar Limit for $e$ . . . . . . . . . 72--73
Harold L. Schoen A Geometric Approach to the Orders of
Infinity . . . . . . . . . . . . . . . . 74--76
Aron Pinker A Note on Derivatives of Polynomials . . 77--78
Rosemary Schmalz, S. P. Complex Numbers as Residue Classes of
Polynomials $ \mod (x^2 + 1) $ . . . . . 78--80
Chris Burditt Two-Pan Weighings . . . . . . . . . . . 80--81
Anonymous Subscription Information . . . . . . . . 82--82
Anonymous Editorial Board . . . . . . . . . . . . ??
Karl J. Smith Pascal's Triangle . . . . . . . . . . . 1--13
H. L. Kung On Particular Solutions of $ P_n(D) Y =
0 $ . . . . . . . . . . . . . . . . . . 14--17
Keith J. Craswell An Interesting Penny Game . . . . . . . 18--25
Michael Olinick Solving Systems of Linear Differential
Equations . . . . . . . . . . . . . . . 26--30
E. A. Maier and
David Maier A Construction of the Real Numbers . . . 31--35
Martin D. Landau and
William R. Jones An Interpolation Question Resolved by
Calculus . . . . . . . . . . . . . . . . 36--39
Ralph C. Williams The Mathematics Laboratory and the
Single Student . . . . . . . . . . . . . 40--47
H. Vernon Price A Doctorate for the Two-Year College
Instructor? . . . . . . . . . . . . . . 48--50
John Wagner and
Howard Jones Group-Based Instruction: The Best Chance
for Success? . . . . . . . . . . . . . . 51--54
Cameron Douthitt The Effects of a Laboratory on
Achievement in College Freshman
Mathematics . . . . . . . . . . . . . . 55--59
Calvin A. Lathan Reviews . . . . . . . . . . . . . . . . 60--69
Anonymous News and Notes . . . . . . . . . . . . . 70--70
Anonymous Calendar of Events . . . . . . . . . . . 71--72
Anonymous Problems and Solutions . . . . . . . . . 73--73
Stewart S. Cairns Topological Regular Solids . . . . . . . 74--76
H. E. Reinhardt Four Theorems About Montana . . . . . . 76--78
Benjamin Greenberg A ``Doodling'' Inequality . . . . . . . 78--79
Anonymous Editorial Board . . . . . . . . . . . . ??
Anonymous Subscription Information . . . . . . . . ??
Colin Clark Some Socially Relevant Applications of
Elementary Calculus . . . . . . . . . . 1--15
G. Baley Price Telescoping Sums and the Summation of
Sequences . . . . . . . . . . . . . . . 16--29
Howard E. Reinhardt Dividing Inheritances . . . . . . . . . 30--33
John M. H. Olmsted Riemann Integration in Ordered Fields 34--40
David R. Duncan and
Bonnie H. Litwiller Checkerboards and Sugar Cubes: Geometric
Counting Patterns . . . . . . . . . . . 41--47
Jack M. Robertson Another Challenge in the Classroom . . . 48--54
Anthony Giangrasso A Flexible Response to Open Admissions 55--58
Bert K. Waits and
Larry C. Elbrink Student Evaluation of Mathematics
Instruction . . . . . . . . . . . . . . 59--66
Donald Perry A Study, Using CUPM Recommendations As
Criteria, of the Academic Preparation of
Two-Year College Teachers . . . . . . . 67--71
Anthony N. Behr Achievement, Aptitude and Attitude in
Mathematics . . . . . . . . . . . . . . 72--74
Anonymous Reviews . . . . . . . . . . . . . . . . 75--81
Anonymous News and Notes . . . . . . . . . . . . . 82--82
Anonymous Calendar of Events . . . . . . . . . . . 83--84
Anonymous Problems and Solutions . . . . . . . . . 85--85
Sidney Penner ab=c . . . . . . . . . . . . . . . . . . 86--87
Frances W. Lewis Teaching Inequalities Involving Absolute
Values . . . . . . . . . . . . . . . . . 87--90
Norman Schaumberger Evaluating $ \int_a^b x^k \, d x $ Where
$k$ Is Any Negative Integer Other Than $
- 1$ . . . . . . . . . . . . . . . . . . 91--93
Anonymous Subscription Information . . . . . . . . 94--94
Anonymous Editorial Board . . . . . . . . . . . . ??
Anonymous Institutional Subscribers . . . . . . . 1--6
W. G. Leavitt Fermat Numbers . . . . . . . . . . . . . 7--10
Rodney D. Gentry Generalizing Rolle's Theorem in
Elementary Calculus . . . . . . . . . . 11--17
Keith J. Craswell How to Find a Needle in a Haystack . . . 18--21
Jean J. Pedersen Plaited Platonic Puzzles . . . . . . . . 22--37
Dale Woods and
Mary Jane Kohlenberg Pascal's $k$-Simplex . . . . . . . . . . 38--43
Marc Swadener On Transformations and Matrices . . . . 44--51
Bert K. Waits and
Jerry L. Silver A New Look at an Old Work Problem . . . 52--55
Shelba Jean Morman An Audio-Tutorial Method of Instruction
vs the Traditional Lecture-Discussion
Method . . . . . . . . . . . . . . . . . 56--61
S. K. Stein Mathematics for the Captured Student . . 62--71
James A. Van Dyke and
Donald C. Willner Reviews . . . . . . . . . . . . . . . . 72--78
Anonymous Calendar of Events . . . . . . . . . . . 79--79
Anonymous News and Notes . . . . . . . . . . . . . 80--80
Erwin Just Problems and Solutions . . . . . . . . . 81--84
John W. LeDuc $ \delta $ As a Function of $ \epsilon
$, A Suggestion for the Calculus Teacher 85--86
Morton J. Hellman Some Applications of the Law of the
Contrapositive . . . . . . . . . . . . . 86--88
F. A. Chimenti Arc Length Revisited . . . . . . . . . . 88--89
Anonymous Editorial Board . . . . . . . . . . . . ??
Anonymous Subscription Information . . . . . . . . ??
Anonymous Institutional Subscribers . . . . . . . 1--6
G. Lenz The Neglected Aspect of Math-Ed: The
Liberal Arts Course . . . . . . . . . . 7--8
Ralph Mansfield The Man-Made World: Cultural vs Remedial
Mathematics . . . . . . . . . . . . . . 9--21
L. H. Lange Maximize $ x (a - x) $ . . . . . . . . . 22--24
Pasquale J. Arpaia Rings, Subrings, Identities and
Homomorphisms . . . . . . . . . . . . . 25--28
J. Maurice Kingston Cyclically Permuted Code: a Variation on
Binary Arithmetic . . . . . . . . . . . 29--36
Pat Semmes A Geometric Approach to Linear
Programming In the Two-Year College . . 37--40
Karl Greger Random Sieving and the Prime Number
Theorem . . . . . . . . . . . . . . . . 41--46
Margaret Maxfield Innovative Evaluation . . . . . . . . . 47--52
Nancy F. Carter and
Marc Swadener A Bibliography of Literature:
Mathematics Education in the Junior and
Community Colleges . . . . . . . . . . . 53--59
Edward B. Wright and
Frank Hacker and
Harry L. Hancock and
Judith Gersting and
Allen R. Angel Reviews . . . . . . . . . . . . . . . . 60--66
Anonymous Calendar of Events . . . . . . . . . . . 67--67
Anonymous News and Notes . . . . . . . . . . . . . 68--68
Anonymous Problems and Solutions . . . . . . . . . 69--72
Norman Schaumberger A Classroom Theorem on Trigonometric
Irrationalities . . . . . . . . . . . . 73--76
Aron Pinker The Equivalence of the Well-Ordering
Principle and Dirichlet's Box Principle 76--77
Lawrence G. Gilligan and
Robert B. Nenno Who Dunnit? . . . . . . . . . . . . . . 78--79
Harold L. Schoen A Further Note on the Orders of Infinity 80--82
Anonymous Subscription Information . . . . . . . . 83--83
Anonymous Editorial Board . . . . . . . . . . . . ??
S. K. Stein Formal Integration: Dangers and
Suggestions . . . . . . . . . . . . . . 1--7
Sidney H. L. Kung An Alternative to Euclidean Algorithm 8--11
Robert Owen Armstrong Construction of an Exercise Involving
Minimum Time . . . . . . . . . . . . . . 12--14
Helmer Junghans Square Functions . . . . . . . . . . . . 15--18
Joseph J. Ettl The Delta Method Approximates the Roots
of Polynomial Equations . . . . . . . . 19--20
Roger G. Lindley The Interpolating Polynomial . . . . . . 21--31
William Mitchell Improving General Education Mathematics 32--38
Donald R. Horner Nonlab, Nonprogrammed, and Nonlecture:
Any Chance? . . . . . . . . . . . . . . 39--44
Wayne L. Miller The Contract Method vs the Traditional
Method of Teaching Developmental
Mathematics to Underachieves: a
Comparative Analysis . . . . . . . . . . 45--49
Paul W. Merritt Some Research Support for A Second
Chance for Beginning Algebra Students 50--54
Lawrence Clar and
Gerald M. Smith and
Peter A. Lindstrom and
Arthur P. Dull and
Olene C. Zacher and
Philip F. Rcichmeider Reviews . . . . . . . . . . . . . . . . 55--59
Anonymous News and Notes . . . . . . . . . . . . . 60--62
Anonymous Calendar of Events . . . . . . . . . . . 63--64
Erwin Just Problems and Solutions . . . . . . . . . 65--67
Roland E. Larson Continuous Deformation of a Polynomial
into Its Derivatives . . . . . . . . . . 68--70
Nathan Hoffman Partitions of the Plane . . . . . . . . 71--73
Joseph C. Bodenrader Mini-Calculus . . . . . . . . . . . . . 74--74
Anonymous Editorial Board . . . . . . . . . . . . ??
Anonymous Subscription Information . . . . . . . . ??
Anonymous Subscription Information . . . . . . . . 1--1
Anonymous Institutional Subscribers . . . . . . . 2--7
Anonymous Editorials . . . . . . . . . . . . . . . 8--8
John C. Wenger Letters to the Editor . . . . . . . . . 9--11
Peter A. Lindstrom A Note on Epsilons and Deltas . . . . . 12--13
Benjamin Greenberg Some Insight into the Convex
Quadrilateral . . . . . . . . . . . . . 14--17
Keith J. Craswell Why Isn't Penny Flipping Fairer? . . . . 18--19
Stewart Venit Interchanging the Order of Integration 20--21
Marc Swadener A Finite Field --- a Finite Geometry and
Triangles . . . . . . . . . . . . . . . 22--25
Norman Schaumberger A Set of Trigonometric Inequalities with
Applications to Maxima and Minima . . . 26--30
Louise Dyson and
Edward B. Wright Pills: Mathematics Instructional Model 31--33
Frank O. Armbruster and
Jean J. Pedersen Bubbles . . . . . . . . . . . . . . . . 34--38
William M. Setek, Jr. Logic: a Logical Elective . . . . . . . 39--40
June P. Wood and
Betty J. Hinman and
Eugene P. Cooper and
H. Eugene Hall and
Amogene F. DeVaney and
S. C. Tefteller and
Alan C. Tucker Reviews . . . . . . . . . . . . . . . . 41--45
Anonymous News and Notices . . . . . . . . . . . . 46--49
Erwin Just Problems and Solutions . . . . . . . . . 50--54
Frederick H. Young Computer Corner . . . . . . . . . . . . 55--57
Norman Schaumberger Some Comments on the Exceptional Case in
a Basic Integral Formula . . . . . . . . 58--58
Anonymous Editorial Board . . . . . . . . . . . . ??
Lawrence Trivieri and
Bill Peters Letters to the Editor . . . . . . . . . 1--3
Arne Broman Computer Computation of Integrals . . . 4--11
David L. Jones A Study of the Coefficient J(n, i) . . . 12--15
Michael A. Topper and
James W. Armstrong A Working Model for Inservice Training 16--18
Donald Perry and
Wayne L. Miller A Suggested Recruiting Project: Math
Contests . . . . . . . . . . . . . . . . 19--21
Lewis H. Coon A Doctor's Degree for Community College
Teachers --- Why? . . . . . . . . . . . 22--26
Bert K. Waits Instructional Videocassettes in
Mathematics . . . . . . . . . . . . . . 27--30
June P. Wood and
Betty J. Hinman and
Cameron Douthitt and
Don Gallagher and
Shelba Morman and
Peter A. Lindstrom Reviews . . . . . . . . . . . . . . . . 31--34
Anonymous News and Notices . . . . . . . . . . . . 35--37
Anonymous Problems and Solutions . . . . . . . . . 38--41
Lawrence G. Gilligan and
Nelson G. Rich Computer Corner . . . . . . . . . . . . 42--48
Louise S. Grinstein Calculus by Mistake . . . . . . . . . . 49--53
Aron Pinker A Generator of Trigonometric Identities 54--55
Anonymous Editorial Board . . . . . . . . . . . . ??
Anonymous Editorials . . . . . . . . . . . . . . . 1--1
William Stenger Cauchy's Inequality and the Least
Squares Line . . . . . . . . . . . . . . 2--4
Walter W. Bolton and
Sterling G. Crim A Linear Integral Transform with a
Simple Kernel . . . . . . . . . . . . . 5--7
L. E. Fuller and
J. D. Logan On the Evaluation of Determinants by
Chi\`o's Method . . . . . . . . . . . . 8--10
Peter A. Lindstrom Survival of the Two-Year College
Mathematics Teacher . . . . . . . . . . 11--13
Clyde A. Bridger Leonardo, His Rabbits, and Other Curiosa 14--20
Vincent J. Motto Mathematical Astronomy . . . . . . . . . 21--26
June P. Wood and
Betty J. Hinman and
Ara B. Sullenberger and
Lawrence Gilligan and
Thomas L. Alexander Reviews . . . . . . . . . . . . . . . . 27--29
Anonymous News and Notices . . . . . . . . . . . . 30--31
Anonymous Problems and Solutions . . . . . . . . . 32--34
Roland E. Larson Graphing a Cubic Using Calculus and a
Computer . . . . . . . . . . . . . . . . 35--40
Anonymous Editorial Board . . . . . . . . . . . . ??
Calvin Lathan Editorial . . . . . . . . . . . . . . . 1--1
David R. Duncan and
Bonnie H. Litwiller Investigations of Linear and Reciprocal
Functions by the Line-to-Line Technique 2--9
Myles Greene Distributivity with Respect to All Four
Rational Operations . . . . . . . . . . 10--12
Richard Wiebe Gödel's Theorem (Part I) . . . . . . . . 13--17
Judith L. Gersting Mathematical Induction: If Student $k$
Understands It, Will Student $ k + 1 $? 18--19
Richard L. Francis Polygons, Both Perfect and Regular . . . 20--21
Judith Harle Hector A Mastery Approach to Mathematical
Literacy . . . . . . . . . . . . . . . . 22--27
June P. Wood and
Betty J. Hinman Reviews . . . . . . . . . . . . . . . . 28--28
Anonymous News & Notices . . . . . . . . . . . . . 29--30
Anonymous Problems and Solutions . . . . . . . . . 31--35
Larry Collister Computer Corner . . . . . . . . . . . . 36--41
Morton Bloomfield and
Frank Lasak Closing the Loopholes . . . . . . . . . 42--44
Erwin Just and
Norman Schaumberger Two More Proofs of a Familiar Inequality 45--45
Anonymous Editorial Board . . . . . . . . . . . . ??
Herbert I. Gross and
Lawrence L. Krajewski and
Ralph P. Boas and
R. P. Boas and
D. H. Erkiletian Letters to the Editor . . . . . . . . . 1--3
Richard Wiebe Gödel's Theorem (Part II) . . . . . . . . 4--7
Thomas J. Brieske Factoring Functions and Relations . . . 8--12
G. L. Alexanderson and
L. F. Klosinski Some Surprising Volumes of Revolution 13--15
Norman Woo On Generalized $h$-Base . . . . . . . . 16--17
David Beran Note on Teaching the Implication . . . . 18--19
Ralph Mansfield Mathematics --- Is It Any of Your
Business? . . . . . . . . . . . . . . . 20--26
June P. Wood and
Betty J. Hinman and
Jean B. Smith and
Cherry Mauk and
R. DeJean and
Terral McKellips Reviews . . . . . . . . . . . . . . . . 27--30
Anonymous News and Notices . . . . . . . . . . . . 31--33
Anonymous Problems and Solutions . . . . . . . . . 34--37
Daniel T. Bleck Computer Corner . . . . . . . . . . . . 38--40
Student Keith Gant and
Dean B. Priest The Countability of the Rationals
Revisited . . . . . . . . . . . . . . . 41--42
David Bender Hyperbolic Functions . . . . . . . . . . 42--45
Anonymous Editorial Board . . . . . . . . . . . . ??
Calvin A. Lathan Editorial . . . . . . . . . . . . . . . 1--1
Saul Birnbaum and
David W. Erbach and
Peter A. Lindstrom Letters to the Editor . . . . . . . . . 2--3
Roland Engdahl and
Karl Greger Random Charity. A Stochastic Sieving
Problem and its Connection with the
Euclidean Algorithm . . . . . . . . . . 4--9
Robert S. Fisk Some Applications of Modeling in
Mathematics for Two-Year Colleges . . . 10--13
Nancy F. Carter A Survey of Mathematics Programs . . . . 14--16
June P. Wood and
Betty J. Hinman and
Lawrence A. Trivieri and
Gerald M. Smith and
Bruce King Reviews . . . . . . . . . . . . . . . . 17--20
William G. Chinn News and Notices . . . . . . . . . . . . 21--23
Anonymous Problems and Solutions . . . . . . . . . 24--28
Samuel Goldberg A Precalculus Unit on Area Under Curves 29--35
Lawrence Sher Solving Whodunits by Symbolic Logic . . 36--38
Aron Pinker An Interesting Use of Generating
Functions . . . . . . . . . . . . . . . 39--45
Anonymous Editorial Board . . . . . . . . . . . . ??
Calvin Lathan Editorial . . . . . . . . . . . . . . . 1--1
Lawrence Sher Letters to the Editor . . . . . . . . . 1--1
L. H. Lange Several Hyperbolic Encounters . . . . . 2--6
Mark D. Galit and
John P. Pace Inter-related Concepts: an Example . . . 7--10
Norman Schaumberger A Geometrical Approach to a Basic Limit 11--12
Orrin G. Cocks The Well-Ordering Principle as an
Alternative to Mathematical Induction in
Our Lower Division Recursive Formula
Proofs . . . . . . . . . . . . . . . . . 13--14
Julian Weissglass Small Groups: an Alternative to the
Lecture Method . . . . . . . . . . . . . 15--20
Andrew Sterrett A Search for Trends among Mathematics
Programs in Small Colleges . . . . . . . 21--23
June P. Wood and
Betty J. Hinman and
Nancy Holder and
James G. Troutman and
Ken Seydel Reviews . . . . . . . . . . . . . . . . 24--26
William G. Chinn News and Notices . . . . . . . . . . . . 27--27
Erwin Just Problems and Solutions . . . . . . . . . 28--32
Thomas M. Green Identities, Inequalities and Equations:
a Computer-Graphical Approach . . . . . 33--37
Lewis G. Maharam and
Edward P. Shaughnessy When Does $ (f g)' = f' g' $? . . . . . 38--39
Anonymous Editorial Board . . . . . . . . . . . . ??
Allen Angel and
Orrin Cocks and
Leonard Feldman Letters to the Editor . . . . . . . . . 1--2
Anneli Lax Linear Algebra, a Potent Tool . . . . . 3--15
W. G. Leavitt An Algorithm and Its Connection with
Abelian Groups . . . . . . . . . . . . . 16--21
Phillip E. Johnson Eighteenth Century British Mathematics 22--27
Eddie R. Williams and
Harold W. Mick Research and Development of Synchronized
Slide-Tape Units for a Mathematics
Laboratory . . . . . . . . . . . . . . . 28--33
Clifford L. Conrad and
Nancy J. Conrad and
Harry B. Higley A New Approach for Computer Mathematics 34--39
June P. Wood and
Betty J. Hinman and
John P. Pace and
Wesley W. Tom Reviews . . . . . . . . . . . . . . . . 40--42
Peter A. Lindstrom Two-Year College News . . . . . . . . . 43--48
Erwin Just Problems and Solutions . . . . . . . . . 49--53
G. Pólya As Their Students See Them . . . . . . . 54--54
James E. McKenna Computation of Repeating Decimals . . . 55--58
R. H. Cowen A Simple Proof of the Reflection
Property for Parabolas . . . . . . . . . 59--60
Anonymous Editorial Board . . . . . . . . . . . . ??
Harold Partin and
John Staib and
Paul Shapiro and
Herbert Peebles Letters to the Editor . . . . . . . . . 1--4
Michael Olinick and
Bruce B. Peterson Darboux's Theorem and Points of
Inflection . . . . . . . . . . . . . . . 5--9
Burt M. Rosenbaum An Integral Approximation Exact for
Fifth-Degree Polynomials . . . . . . . . 10--14
Ann D. Hollev Functional Notation --- an Intuitive
Approach . . . . . . . . . . . . . . . . 14--15
Cliff Long A Flexible Model for Peak, Ridge and
Pass . . . . . . . . . . . . . . . . . . 16--17
Larry F. Bennett Another Note on Epsilons and Deltas . . 18--18
Clifford Sloyer What Is an Application of Mathematics? 19--26
Gerald E. Lenz History in the Mathematics Curriculum 27--28
Helen B. Siner The Open University . . . . . . . . . . 28--32
William F. Steger and
Gretchen Willging Modularizing Liberal Arts Mathematics:
an Experiment . . . . . . . . . . . . . 33--37
June P. Wood and
Betty J. Hinman and
Donald E. Brown and
Mary Ann De Vincenzo and
Ralph Mansfield Reviews . . . . . . . . . . . . . . . . 38--40
Peter A. Lindstrom Two-Year College News . . . . . . . . . 41--46
Anonymous Problems and Solutions . . . . . . . . . 47--50
G. Pólya As Their Students See Them . . . . . . . 51--51
Pasquale Scopelliti and
Herbert Peebles Computer Corner . . . . . . . . . . . . 52--54
Gene Zirkel Closing the Loopholes in ``Closing the
Loopholes'' . . . . . . . . . . . . . . 55--56
Larry F. Bennett Another Note on ``Closing the
Loopholes'' . . . . . . . . . . . . . . 56--58
Anonymous Editorial Board . . . . . . . . . . . . ??
Stewart M. Venit Remarks Concerning the Delta Method for
Approximating Roots . . . . . . . . . . 1--3
Robert G. Stein Exploring the Gaussian Integers . . . . 4--10
Richard C. Weimer Can the Complex Numbers Be Ordered? . . 10--12
Corrinne J. Brase and
Charles H. Brase Basic Algebra in a Balanced
Lecture-Program Format . . . . . . . . . 13--17
Irwin K. Feinstein The Doctor of Arts Degree in Mathematics
University of Illinois at Chicago Circle 18--20
Gordon D. Prichett The Game of Sprouts . . . . . . . . . . 21--25
June P. Wood and
Betty J. Hinman and
Peter A. Lindstrom and
Marilyn F. Semrau and
Suzanne Brown (Donald) Reviews . . . . . . . . . . . . . . . . 26--28
Anonymous Two-Year College News . . . . . . . . . 29--32
Anonymous Problems and Solutions . . . . . . . . . 33--37
G. Pólya As Their Students See Them . . . . . . . 38--38
Joe Dan Austin Computer Corner . . . . . . . . . . . . 39--42
John W. Dawson, Jr. Some Ridge-Length Problems . . . . . . . 43--45
John T. Varner III Comparing a$^b$ and b$^a$ Using
Elementary Calculus . . . . . . . . . . 46--46
Gerard P. Protomastro An Alternative Proof of the Equality of
the Mixed Partial Derivatives . . . . . 47--48
James E. McKenna Interpolation and Square Roots . . . . . 49--50
Anonymous Editorial Board . . . . . . . . . . . . ??
Calvin A. Lathan Editorial . . . . . . . . . . . . . . . 3--3
Hilda Duncan and
David Emery Finite Euclidean Geometries of Order $p$ 4--10
David A. Birnbaum and
Northrup Fowler III An Elementary Result on Derivatives . . 10--11
Janet B. Pomeranz Counterexamples from the Algebra of
Polynomials over a Nonfield . . . . . . 11--14
Janet E. Ford and
Douglas B. McLeod Flow Charts in Mathematics Classes for
Elementary School Teachers . . . . . . . 15--19
Larry J. Stephens Getting the Students Involved in the
Elementary Statistics Course . . . . . . 19--21
R. C. Pierce, Jr. A Brief History of Logarithms . . . . . 22--26
Square Partee and
Eric Halsey Discovery Method Algebra at the
University of Washington . . . . . . . . 27--29
Barbara J. Lederman The Community College Basic Mathematics
Course . . . . . . . . . . . . . . . . . 29--34
June P. Wood and
Betty J. Hinman and
Peter Lindstrom and
Mary Ann DeVincenzo Reviews . . . . . . . . . . . . . . . . 35--37
Anonymous Two-Year College News . . . . . . . . . 38--41
Anonymous Problems and Solutions . . . . . . . . . 42--46
Glenn D. Allinger Computer Corner . . . . . . . . . . . . 47--50
Roy E. Myers Some Elementary Results Related to the
Mean Value Theorem . . . . . . . . . . . 51--53
Anonymous Editorial Board . . . . . . . . . . . . ??
Harold L. Dorwart Can this Polynomial Be Factored? . . . . 67--72
Debra Charpentier Women Mathematicians . . . . . . . . . . 73--79
Nancy F. Carter What's It Good for? . . . . . . . . . . 79--80
Donald Cohen The Sequencing of Instructional
Activities in Written Materials . . . . 81--87
June P. Wood and
Betty J. Hinman and
Leland D. Graber and
Dennis M. Rodriguez Reviews . . . . . . . . . . . . . . . . 88--89
Anonymous Two-Year College News . . . . . . . . . 90--94
Anonymous Problems and Solutions . . . . . . . . . 95--100
Willjam S. Dorn Computer Corner . . . . . . . . . . . . 101--105
V. N. Murty Independence and Intuition . . . . . . . 106--107
Robert C. Crawford Using Inverse Functions in Integration 107--109
Anonymous Editorial Board . . . . . . . . . . . . ??
Thomas R. Thomson and
Lester Lange Dean Letters to the Editor . . . . . . . . . 131--131
Donn C. Sandell and
F. Max Stein Factorization of Operators of Second
Order Linear Homogeneous Ordinary
Differential Equations . . . . . . . . . 132--141
Norman Schaumberger Some Consequences of a Property of the
Centroid of a Triangle . . . . . . . . . 142--144
Carl G. Wagner Newton's Inequality and a Test for
Imaginary Roots . . . . . . . . . . . . 145--147
Lawrence Sher The Perfect Curve: at Least for Grades 148--152
Kay Dundas Quasi-Pythagorean Triples for an Oblique
Triangle . . . . . . . . . . . . . . . . 152--155
Betsey Whitman and
Donald Cook Operational and Intuitive Algebra . . . 155--161
Eric J. Nelson A Machine-Oriented Technique for the
Complete Solution of Linear Systems . . 161--164
June P. Wood and
Betty J. Hinman and
John McGregor and
Suzanne Brown Reviews . . . . . . . . . . . . . . . . 165--167
Anonymous Two-Year College News . . . . . . . . . 168--176
Anonymous Problems and Solutions . . . . . . . . . 177--181
Samuel W. Spero and
Mary Koehler Computer Corner . . . . . . . . . . . . 182--187
Robert Rosenfeld A Helpful Device: or One More Use for
Pascal's Triangle . . . . . . . . . . . 188--191
Anonymous Editorial Board . . . . . . . . . . . . ??
Hugh Ouellette and
Gordon Bennett Stirling's Triangle of the First
Kind-Absolute Value Style . . . . . . . 195--202
James A. Burns Some Effects of Rationing . . . . . . . 203--206
Frieda Zames Surface Area and the Cylinder Area
Paradox . . . . . . . . . . . . . . . . 207--211
Charles R. Burton and
Wanda A. Marosz The Construction and Uses of CATIA, a
Computerized Mathematics Testbank . . . 212--216
Robert C. Sanger A Transfer Level Computer Calculus
Sequence . . . . . . . . . . . . . . . . 216--218
Michael E. Greenwood Two Factors Involved in Successful
Individualized Mathematics Programs . . 219--222
Allen H. Holmes and
Walter Sanders and
John LeDuc Statistical Inference for the General
Education Student-It Can Be Done . . . . 223--230
June P. Wood and
Betty J. Hinman and
David Farnsworth and
Samiha Mourad Reviews . . . . . . . . . . . . . . . . 231--235
Anonymous Two-Year College News . . . . . . . . . 236--239
Anonymous Problems and Solutions . . . . . . . . . 240--243
Thomas P. Dence Computer Corner . . . . . . . . . . . . 244--246
Ray F. Snipes On the Definition of Implication:
Classroom Discussion and Justification 247--252
Roland H. Lamberson An Environmental Problem . . . . . . . . 252--253
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald Cohen Letters to the Editor . . . . . . . . . 259--259
Jay E. Strum Binomial Matrices . . . . . . . . . . . 260--266
Kenneth Slonneger Types of Relations . . . . . . . . . . . 267--269
Judith L. Gersting and
Joseph E. Kuczkowski Why and How to Use Small Groups in the
Mathematics Classroom . . . . . . . . . 270--274
James H. Jordan An Elementary Construction of the Common
Log Tables . . . . . . . . . . . . . . . 274--278
Allen R. Angel An Interesting Approach to $ \delta $, $
\epsilon $ Proofs . . . . . . . . . . . 278--280
June P. Wood and
Betty J. Hinman and
David E. Moxness and
Jean B. Smith Reviews . . . . . . . . . . . . . . . . 281--285
Anonymous Two-Year College News . . . . . . . . . 286--291
Anonymous Problems and Solutions . . . . . . . . . 292--295
Edwin G. Landauer Computer Corner: Methods of Random
Number Generation . . . . . . . . . . . 296--303
John Taylor Varner III Discovering a Calculus Theorem . . . . . 304--304
Anonymous Editorial Board . . . . . . . . . . . . ??
W. Roy Fraser and
Dorothy Buerk and
Herta T. Freitag Letters to the Editor . . . . . . . . . 3--5
Nathan Hoffman Some New Ways of Solving a Coin Tossing
Problem . . . . . . . . . . . . . . . . 6--10
Richard Plagge Fractions Without Quotients: Arithmetic
of Repeating Decimals . . . . . . . . . 11--15
Norman Schaumberger A Calculus Proof of the
Arithmetic--Geometric Mean Inequality 16--17
Charles M. Bundrick and
David L. Sherry A Note on the Principle of Mathematical
Induction . . . . . . . . . . . . . . . 17--18
Andris Niedra Geometric Series on the Gridiron . . . . 18--20
George Pólya Guessing and Proving . . . . . . . . . . 21--27
Robert L. Heiny The Use of Sports Data for Integrating
Topics in Introductory Statistics . . . 28--33
Wayne Andrepont and
Peter Dickinson Classroom Demonstration of a Confidence
Interval . . . . . . . . . . . . . . . . 34--36
Truman Botts Two-Year College News . . . . . . . . . 37--39
Anonymous Problems and Solutions . . . . . . . . . 40--45
Louise S. Grinstein A Note on Infinite Series . . . . . . . 46--47
Jay I. Miller Differentiating Area and Volume . . . . 47--48
Anonymous Editorial Board . . . . . . . . . . . . ??
Thomas J. Brieske Mapping, Diagrams, Continuous Functions
and Derivatives . . . . . . . . . . . . 67--72
James E. Carpenter Note on L'Hôpital's Rule for the
Indeterminate Form $ \infty / \infty $ 73--74
Richard L. Francis A Note on Angle Construction . . . . . . 75--80
Ann D. Holley A Question of Interest . . . . . . . . . 81--83
June P. Wood and
Betty J. Hinman and
John Niman Reviews . . . . . . . . . . . . . . . . 84--89
Anonymous Two-Year College News . . . . . . . . . 90--94
Anonymous Problems and Solutions . . . . . . . . . 95--100
James G. Troutman Computer Corner . . . . . . . . . . . . 101--103
Alan H. Schoenfeld A Simple Antidifferentiation Technique 104--105
Peter A. Lindstrom A Note on the Integral Test . . . . . . 105--106
R. R. Baldino A Geometrical Proof of Cramer's Rule . . 106--107
Anonymous Editorial Board . . . . . . . . . . . . ??
Marie Loftus Letters to the Editor . . . . . . . . . 131--131
Judithlynne Carson Fibonacci Numbers and Pineapple
Phyllotaxy . . . . . . . . . . . . . . . 132--136
Bruce S. Babcock and
John W. Dawson, Jr. A Neglected Approach to the Logarithm 136--140
David A. Smith The Homicide Problem Revisited . . . . . 141--145
John Sodano and
Arthur Yaspan A Neglected Probability Formula . . . . 145--147
Ralph Mansfield Applicable Mathematics in Two Year
Colleges . . . . . . . . . . . . . . . . 148--153
John Pace A Rational Approach to Fractions . . . . 154--158
Carolyn T. MacDonald Introductory Mathematics and the Adult
Woman Student . . . . . . . . . . . . . 158--161
Bert K. Waits Classroom Applications of the
Inexpensive Hand-Held Calculator . . . . 162--166
June P. Wood and
Betty J. Hinman and
Jean Lane and
Donald E. Brown Reviews . . . . . . . . . . . . . . . . 167--170
Anonymous Two-Year College News . . . . . . . . . 171--175
Anonymous Problems and Solutions . . . . . . . . . 176--181
Abdus Sattar Gazdar Computer Corner . . . . . . . . . . . . 182--185
Lawrence Sher Boolean Algebra as a Proof Paradigm . . 186--190
Thomas W. Shilgalis Flow Chart for Infinite Series . . . . . 191--191
Anonymous Editorial Board . . . . . . . . . . . . ??
Henry L. Alder A Headquarters Building for the
Association . . . . . . . . . . . . . . 195--202
Richard Guy and
Leonard Gillman and
Marjorie A. Fitting Letters to the Editor . . . . . . . . . 203--204
Stephen J. Milles and
Henry J. Schultz Some Functional Equations for the
Calculus Student . . . . . . . . . . . . 205--209
Benjamin Burrell and
Jessie Ann Engle and
Henry C. Nixt Experiment and Conjecture in
Mathematics: a Discovery Course for
College Freshmen and Sophomores . . . . 210--215
Charles G. Moore Completing the Square --- a Laboratory
Approach . . . . . . . . . . . . . . . . 215--218
Charles D. Friesen A Look at General Education Mathematics
Programs . . . . . . . . . . . . . . . . 218--221
June P. Wood and
Betty J. Hinman and
Frank Swetz Reviews . . . . . . . . . . . . . . . . 222--227
Anonymous Two-Year College News . . . . . . . . . 228--235
Anonymous Problems and Solutions . . . . . . . . . 236--242
Satish K. Janardan and
Konanur G. Janardan Computer Corner . . . . . . . . . . . . 243--248
Jane I. Robertson Algorithms for Finding Maturity Value in
Compound Interest Problems . . . . . . . 249--251
Anonymous Editorial Board . . . . . . . . . . . . ??
Tom Brieske and
Johnny Lott The Motion Geometry of a Finite Plane 259--266
Nathan Hoffman Binary Grids and a Related Counting
Problem . . . . . . . . . . . . . . . . 267--272
W. K. Viertel An Interesting Practical Application of
Solid Analytic Geometry . . . . . . . . 273--275
Gail B. Mounteer and
Robert J. Cermele The Role of the Instructor in the
Individualized Classroom . . . . . . . . 276--281
William E. Haver Developing Skills in College Algebra ---
a Mastery Approach . . . . . . . . . . . 282--287
June P. Wood and
Betty J. Hinman and
Mary Ann De Vincenzo and
Marilyn F. Semrau Reviews . . . . . . . . . . . . . . . . 288--293
Anonymous Two-Year College News . . . . . . . . . 294--296
Anonymous Problems and Solutions . . . . . . . . . 297--302
Charles John Acker and
Joe Frank Allison Computer Corner . . . . . . . . . . . . 303--308
Charles G. Moore The Anatomy of the Stupid Error . . . . 309--310
Anonymous Editorial Board . . . . . . . . . . . . ??
Don Albers Editorial . . . . . . . . . . . . . . . 2--2
Kenneth R. Rebman The Pigeonhole Principle (What it is,
how it works, and how it applies to map
coloring) . . . . . . . . . . . . . . . 3--13
G. L. Alexanderson George Pólya Interviewed on His Ninetieth
Birthday . . . . . . . . . . . . . . . . 13--19
James E. Schultz and
Bert K. Waits Computers & Calculators . . . . . . . . . 20--27
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 28--29
Ross A. Honsberger Mathematical Gems . . . . . . . . . . . 30--32
Warren Page Classroom Capsules . . . . . . . . . . . 33--39
G. L. Alexanderson Classics Revisited . . . . . . . . . . . 40--42
Peter A. Lindstrom and
Shelba Jean Morman and
James C. Kropa Book Reviews . . . . . . . . . . . . . . 43--48
Bruce King The Signpost: News & Commentary . . . . . 49--50
Henry L. Alder Establishment of the Archives of
American Mathematics . . . . . . . . . . 51--52
Anonymous Problems . . . . . . . . . . . . . . . . 52--57
Anonymous Guidelines for Prospective TYCMJ Authors 57--58
Anonymous Letters and Late-Breaking News . . . . . 59--60
Anonymous Editorial Board . . . . . . . . . . . . ??
R. P. Boas Travelers' Surprises . . . . . . . . . . 82--88
John Staib Some Pre-Calculus Algebra . . . . . . . 89--95
Mangho Ahuja On Sum-Guessing . . . . . . . . . . . . 95--99
Hugh Ouellette and
Gordon Bennett The Discovery of a Generalization: an
Example in Problem Solving . . . . . . . 100--106
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 107--107
Ross Honsberger Mathematical Gems . . . . . . . . . . . 108--111
Warren Page and
Elmar Zemgalis and
David H. Anderson and
Norman Schaumberger and
Alban J. Roques and
V. N. Murty and
Warren B. Gordon and
Harold D. Shane Classroom Capsules . . . . . . . . . . . 112--118
G. L. Alexanderson Classics Revisited . . . . . . . . . . . 119--122
Peter A. Lindstrom and
Donald C. Fuller Book Reviews . . . . . . . . . . . . . . 123--126
Erwin Just Problems . . . . . . . . . . . . . . . . 127--131
Bruce King The Signpost: News & Commentary . . . . . 132--135
Anonymous Letters and Late-Breaking News . . . . . 135--135
Robert McKelvey The Two-Year Colleges and the Graduate
Schools: The Teachers' Perspective . . . 136--142
Wendell H. Fleming 1978 AMS Survey: Two-year College Report 143--144
Anonymous Editorial Board . . . . . . . . . . . . ??
Ivan Niven An Ellipse Problem Beyond the Reach of
Calculus . . . . . . . . . . . . . . . . 162--168
Bill Leonard and
Harris S. Shultz Triangular Squares . . . . . . . . . . . 169--171
G. L. Alexanderson An Interview with Morris Kline: Part 1 172--178
Philip D. Straffin, Jr. Using Integrals to Evaluate Voting Power 179--181
Robert Nelson Pictures, Probability, and Paradox . . . 182--190
Ann D. Holley Mathematics in Seventeen Three-Hour
Lessons: a Challenge . . . . . . . . . . 191--192
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 193--194
Ross Honsberger Mathematical Gems . . . . . . . . . . . 195--197
Warren Page and
J. P. King and
W. G. Leavitt and
David Beran and
R. S. Luthar and
Stephen A. Book and
Lawrence Sher Classroom Capsules . . . . . . . . . . . 197--204
Peter A. Lindstrom and
Elaine Johnson Tatham and
Charles Miller Book Reviews . . . . . . . . . . . . . . 205--209
Erwin Just Problems . . . . . . . . . . . . . . . . 210--217
Bruce King The Signpost: News & Commentary . . . . . 218--220
Anonymous Letters and Late-Breaking News . . . . . 221--222
Anonymous Editorial Board . . . . . . . . . . . . ??
Irving Joshua Matrix and
Peter Renz Martin Gardner: Defending the Honor of
the Human Mind . . . . . . . . . . . . . 227--232
Anthony Barcellos A Conversation With Martin Gardner . . . 233--244
James C. Frauenthal and
Thomas L. Saaty Foresight--Insight--Hindsight . . . . . 245--254
George Pólya More on Guessing and Proving . . . . . . 255--258
G. L. Alexanderson An Interview with Morris Kline: Part 2 259--264
Ralph P. Boas Jazz, Literature, and the Teaching of
Mathematics . . . . . . . . . . . . . . 264--265
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 266--269
Ross Honsberger Mathematical Gems . . . . . . . . . . . 271--276
Warren Page and
Norman Schaumberger An Alternate Approach to the Derivatives
of the Trigonometric Functions . . . . . 276--277
Harris S. Shultz An Expected Value Problem . . . . . . . 277--278
Warren Page Questions In the Round --- an Effective
Barometer of Understanding . . . . . . . 278--279
Allen Kroopnick How Good is the ``Rule of 72''? . . . . 279--280
Jack C. Slay and
J. L. Solomon A Note on the Cauchy--Schwarz Inequality 280--283
G. L. Alexanderson Classics Revisited . . . . . . . . . . . 283--286
Peter A. Lindstrom and
Henry J. Ricardo and
Barnabas Hughes O. F. M. Book Reviews . . . . . . . . . . . . . . 287--292
Erwin Just Problems . . . . . . . . . . . . . . . . 293--299
Bruce King The Signpost: News & Commentary . . . . . 299--301
Charles H. Jepsen Billiard Balls and a Number Theory
Result . . . . . . . . . . . . . . . . . 306--312
Barnabas B. Hughes Polygonal Roots . . . . . . . . . . . . 313--318
Henry L. Alder The Use of Generating Functions to
Discover and Prove Partition Identities 318--329
Stephen A. Book Why $ n - 1 $ in the Formula for the
Sample Standard Deviation? . . . . . . . 330--333
Zalman Usiskin Products of Sines . . . . . . . . . . . 334--340
Alban J. Roques Computers & Calculators . . . . . . . . . 340--343
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 343--371
Ross Honsberger Mathematical Gems . . . . . . . . . . . 344--347
Warren Page and
Warren B. Gordon Distance from a Point to a Line . . . . 348--349
Michael W. Chamberlain Coin-Tossing Problem Revisited . . . . . 349--350
C. Mus\`es Geometric Interpretations of $ \Sin
\varphi_1 + \Sin \varphi_2 = 1 $ . . . . 350--351
Lawrence Sher and
Warren Page Bounds for the Sum of Absolute Standard
Scores . . . . . . . . . . . . . . . . . 351--353
John Staib and
Howard Anton A Discovery Approach to Integration by
Parts . . . . . . . . . . . . . . . . . 353--354
Leo Chosid Queries . . . . . . . . . . . . . . . . 354--355
Peter A. Lindstrom and
Kenneth E. Martin Book Reviews . . . . . . . . . . . . . . 355--358
Erwin Just Problems . . . . . . . . . . . . . . . . 359--367
Bruce King The Signpost: News & Commentary . . . . . 367--370
Dave Logothetti Super Bat Meets the Word Problem . . . . 371--371
Joel Brenner and
Ralph P. Boas and
Richard K. Williams Letters and Late-Breaking News . . . . . 372--374
Anonymous Editorial Board . . . . . . . . . . . . ??
Dave Logothetti An Interview with H. S. M. Coxeter, the
King of Geometry . . . . . . . . . . . . 2--19
Jean J. Pedersen Geometry Is Alive and Well: The Coxeter
Symposium in Toronto . . . . . . . . . . 19--25
G. D. Chakerian Circles and Spheres . . . . . . . . . . 26--41
George McCarty Computers & Calculators . . . . . . . . . 42--48
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 48--49
V. N. Murty A Note on the Derivative of a Composite
Function . . . . . . . . . . . . . . . . 50--50
P. S. Chee and
S. T. Chin On the General Power Function . . . . . 51--51
Kenneth R. Kundert Correlation --- a Vector Approach . . . 52--52
Konanur G. Janardan Further Observations on ``A Neglected
Probability Formula'' . . . . . . . . . 52--54
Harry Sedinger Derivatives Without Limits . . . . . . . 54--55
Peter A. Lindstrom and
Klaus Galda Book Reviews . . . . . . . . . . . . . . 56--58
Anonymous Telegraphic Reviews . . . . . . . . . . 59--60
Erwin Just Problems . . . . . . . . . . . . . . . . 61--65
Bruce King The Signpost: News & Commentary . . . . . 66--67
Anonymous Editorial Board . . . . . . . . . . . . ??
Ralph Boas Snowfalls and Elephants, Pop Bottles and
$ \pi $ . . . . . . . . . . . . . . . . 82--89
V. N. Murty Integration by Parts . . . . . . . . . . 90--94
J. Michael Shaughnessy Applications of Intermediate Algebra: a
Possible Alternative . . . . . . . . . . 94--101
John W. Dawson, Jr. Wavefronts, Box Diagrams, and the
Product Rule: a Discovery Approach . . . 102--106
R. S. Luthar Luddhar's Method of Solving a Cubic
Equation with a Rational Root . . . . . 107--110
Anonymous Computers & Calculators . . . . . . . . . 110--110
Sarah Brooks Computer Solution of Alphametics . . . . 111--114
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 114--115
Ross Honsberger Mathematical Gems . . . . . . . . . . . 116--119
Robert Donaghey and
Warren Gordon An Investment Approach to Geometric
Series . . . . . . . . . . . . . . . . . 120--121
Kenneth R. Kundert Why Not Teach Synthetic Multiplication? 121--122
B. H. Bissinger Stochastic Independent Versus Intuitive
Independence . . . . . . . . . . . . . . 122--123
Carl P. McCarty A Rational Approximation to $ \sqrt {n}
$ . . . . . . . . . . . . . . . . . . . 123--124
Ervin Y. Rodin Extending Bernoulli's Inequality . . . . 124--126
Peter A. Lindstrom and
Leon Bankoff Book Reviews . . . . . . . . . . . . . . 127--128
Anonymous Telegraphic Reviews . . . . . . . . . . 128--130
Erwin Just Problems . . . . . . . . . . . . . . . . 131--141
Bruce King The Signpost: News Commentary . . . . . 142--144
Lester H. Lange I.C.M. Helsinki --- Some Personal Notes 144--146
Anonymous Letters and Late-Breaking News . . . . . 146--149
Anonymous Editorial Board . . . . . . . . . . . . ??
Jean J. Pedersen The Challenge of Classifying Polyhedra 162--173
Peter Hilton Math Anxiety: Some Suggested Causes and
Cures . . . . . . . . . . . . . . . . . 174--188
Anonymous Computers & Calculators . . . . . . . . . 188--188
E. D. McCune and
R. G. Dean and
W. D. Clark Calculators to Motivate Infinite
Composition of Functions . . . . . . . . 189--195
Ross Honsberger Mathematical Gems . . . . . . . . . . . 196--200
David H. Anderson Elementary Derivation of a Formula for
Approximating $ n! $ . . . . . . . . . . 201--202
Norman Schaumberger A Precalculus Approximation of $ n! $ 202--204
W. J. Hall An Expected Value Problem Revisited . . 204--205
Leo Chosid A Quick Test for Rational Roots of a
Polynomial . . . . . . . . . . . . . . . 205--206
Thomas A. McCullough A Note on the Vector Triple Product . . 206--207
Erwin Just Problems . . . . . . . . . . . . . . . . 208--214
Bruce King The Signpost: News Commentary . . . . . 214--216
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 216--217
Peter A. Lindstrom and
Sarah Christiansen Book Reviews . . . . . . . . . . . . . . 218--221
Wendell H. Fleming Two-Year College Survey . . . . . . . . 222--222
Anonymous Editorial Board . . . . . . . . . . . . ??
G. L. Alexanderson An Interview with Constance Reid . . . . 226--238
F. Max Stein The Curve Parallel to a Parabola is not
a Parabola: Parallel Curves . . . . . . 239--246
Peter Hilton Math Anxiety: Some Suggested Causes and
Cures: Part 2 . . . . . . . . . . . . . 246--251
Anonymous Computers and Calculators . . . . . . . 251--251
Stanley G. Wayment Another Question of Interest . . . . . . 252--254
Philip J. Davis Mathematics by Fiat? . . . . . . . . . . 255--263
André L. Yandl Delta, Epsilon, and Polynomials . . . . 263--266
Michael J. Thibodeaux The Lighter Side . . . . . . . . . . . . 267--267
V. N. Murty How Close are the Riemann Sums to the
Integral They Approximate? . . . . . . . 268--270
Stewart Venit and
Richard Katz An Analytic Geometry Approach to the
Least Squares Line of Best Fit . . . . . 270--272
Iain T. Adamson A Combinatorial Proof of Euler's Formula 272--273
Norman Schaumberger Another Derivation of a Double
Inequality . . . . . . . . . . . . . . . 273--273
Lehi T. Smith Orthogonal Basis: a Computational
Alternative . . . . . . . . . . . . . . 274--274
Erwin Just Problems . . . . . . . . . . . . . . . . 275--280
Anonymous Telegraphic Reviews . . . . . . . . . . 281--282
Bruce King The Signpost: News & Commentary . . . . . 283--285
Anonymous Editorial Board . . . . . . . . . . . . ??
Gerald D. Brazier What Are the Odds? --- Constructing
Competition Probabilities . . . . . . . 290--295
Andrejs Dunkels and
Lars-Erik Persson Creative Teaching by Mistakes . . . . . 296--300
Martin Berman Altitudes ad Infinitum . . . . . . . . . 300--304
Ross Honsberger Mathematical Gems . . . . . . . . . . . 305--312
James R. Choike The Pentagram and the Discovery of an
Irrational Number . . . . . . . . . . . 312--316
Stewart Venit Conic Section or Degenerate Form --- a
Simple Test . . . . . . . . . . . . . . 316--319
Cliff Long and
Vic Norton Computers & Calculators . . . . . . . . . 320--325
Charles G. Moore An Error-Detecting Check by Substitution 326--327
L. N. Somanchi An Arithmetic Description of the
Dihedral Group . . . . . . . . . . . . . 327--329
Mary Powderly A Geometric Proof of Cauchy's
Generalized Law of the Mean . . . . . . 329--330
Leo Chosid Trigonometric Solutions to the Quadratic
Equation . . . . . . . . . . . . . . . . 330--331
David L. Pugh An Application from Combinatorics to
Dice-Sum Frequencies . . . . . . . . . . 331--333
David Hsu Another Way of Looking at $ n! $ . . . . 333--335
Erwin Just Problems . . . . . . . . . . . . . . . . 335--341
Peter A. Lindstrom and
S. S. Holland, Jr. Book Reviews . . . . . . . . . . . . . . 341--345
Bruce King The Signpost: News & Commentary . . . . . 346--347
Anonymous Editorial Board . . . . . . . . . . . . ??
Thomas Butts Fixed Point Iteration --- an Interesting
Way to Begin a Calculus Course . . . . . 2--7
Leonard G. Swanson and
Rodney T. Hansen Mathematical Induction or ``What Good Is
All This Stuff if We Are Going to Assume
It's True Anyway?'' . . . . . . . . . . 8--12
Richard J. Friedlander Factoring Factorials . . . . . . . . . . 12--20
Byron L. McAllister and
J. Eldon Whitesitt Is $ \Ln $ the Other Shoe? . . . . . . . 20--23
Anonymous Computers & Calculators . . . . . . . . . 23--23
Michael Ratliff A Geometric Motivation of Fermat's
Factoring Method . . . . . . . . . . . . 24--27
Jack C. Slay and
J. L. Solomon A Mean Generating Function . . . . . . . 27--29
David H. Anderson Obtaining a Numerical Estimate for $e$ 30--33
Robert Osserman and
Gideon Schwartz Geometry is Dead . . . . . . . . . . . . 33--33
Ross Honsberger Mathematical Gems . . . . . . . . . . . 34--40
Shlomo Libeskind Summation of Finite Series --- a Unified
Approach . . . . . . . . . . . . . . . . 41--50
Lawrence Sher and
David Sher Some Conjectures on Fermat's Last
Conjecture . . . . . . . . . . . . . . . 51--52
Norman Schaumberger A Coordinate Geometry Evaluation of $ |
\tan (A - B)| $ . . . . . . . . . . . . 52--54
Garfield C. Schmidt Uniqueness of Power Series
Representations . . . . . . . . . . . . 54--56
Leo Chosid Compounding Energy Savings . . . . . . . 56--57
Penelope Barlow An Alternative Proof to Dirac's Theorem 57--58
Peter A. Lindstrom and
Marilyn Mays Gilchrist and
Henry Africk Book Reviews . . . . . . . . . . . . . . 58--61
Anonymous Telegraphic Reviews . . . . . . . . . . 61--62
Erwin Just Problems . . . . . . . . . . . . . . . . 63--68
Bruce King The Signpost: News & Commentary . . . . . 68--69
Anonymous Sidney Penner --- In Memoriam . . . . . 69--69
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers Polite Applause for a Proof of One of
the Great Conjectures of Mathematics:
What Is a Proof Today? . . . . . . . . . 82--82
Peter Renz Mathematical Proof: What It Is and What
It Ought to Be . . . . . . . . . . . . . 83--103
Yu. I. Manin A Digression on Proof . . . . . . . . . 104--107
John Mitchem On the History and Solution of the
Four-Color Map Problem . . . . . . . . . 108--116
Anonymous Euclid's \booktitleElements . . . . . . 117--133
Kenneth Appel and
Wolfgang Haken The Nature of Proof: Limits and
Opportunities . . . . . . . . . . . . . 118--119
Thomas Tymoczko Computer Use to Computer Proof: a
Rational Reconstruction . . . . . . . . 120--125
Klaus Galda An Informal History of Formal Proofs:
From Vigor to Rigor? . . . . . . . . . . 126--140
R. P. Boas Nevertheless, Let's Get on with the Job 141--142
Anonymous Telegraphic Reviews . . . . . . . . . . 142--144
K. R. S. Sastry Distance From a Point to a Line . . . . 146--147
James Chew An Alternative Approach to the Vibrating
String Problem . . . . . . . . . . . . . 147--149
Man-Keung Siu From an Inequality to Inversion . . . . 149--151
John Huber Partial and Semipartial Correlation ---
a Vector Approach . . . . . . . . . . . 151--153
Erwin Just Problems . . . . . . . . . . . . . . . . 154--162
Bruce King The Signpost: News & Commentary . . . . . 163--164
Anonymous Editorial Board . . . . . . . . . . . . ??
Ralph P. Boas Who Needs Those Mean-Value Theorems,
Anyway? . . . . . . . . . . . . . . . . 178--181
Anthony Barcellos An Interview with Stan Ulam . . . . . . 182--189
Herbert L. Holden Applying Complex Arithmetic . . . . . . 190--194
Sherman K. Stein Teachers, Clocks, and Students . . . . . 195--198
Denis R. Lichtman Computers & Calculators . . . . . . . . . 199--203
Warren Page and
Richard Johnsonbaugh and
E. F. Schuster Corrections to an Earlier Capsule . . . 204--206
Gerald E. Gannon Visual Application of $ \Sin (\theta_1 +
\theta_2) = \Sin \theta_1 \Cos \theta_2
+ \Cos \theta_1 \Sin \theta_2 $ . . . . 206--206
Ruma Falk Another Look at the Mean, Median, and
Standard Deviation . . . . . . . . . . . 207--208
Gerald Lenz Some Sum of Sums . . . . . . . . . . . . 208--209
V. N. Murty On Dice-Sum Frequencies . . . . . . . . 209--211
Erwin Just Problems . . . . . . . . . . . . . . . . 212--218
Bruce King The Signpost: News & Commentary . . . . . 219--221
Helen D. Bourgeois Book Reviews . . . . . . . . . . . . . . 222--223
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 223--224
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers ``Geometry Is Alive and Well and Living
in Paris Under an Assumed Name'' . . . . 226--226
J. Dieudonné The Universal Domination of Geometry . . 227--231
Branko Grünbaum Shouldn't We Teach \bf GEOMETRY? . . . . 232--238
Robert Osserman Structure vs. Substance: The Fall and
Rise of Geometry . . . . . . . . . . . . 239--246
Dan Wheeler and
David Sklar A Space-Filling Torus . . . . . . . . . 246--248
G. L. Alexanderson An Interview with Paul Erd\Hos . . . . . 249--259
Eugene M. Levin Computers & Calculators . . . . . . . . . 260--266
Warren Page and
Man-Keung Siu Inventor's Paradox . . . . . . . . . . . 267--267
Ann D. Holley Integration by Geometric Insight --- a
Student's Approach . . . . . . . . . . . 268--270
Barbara Turner Point-and-Line Proof for the Sum of the
Cubes . . . . . . . . . . . . . . . . . 270--271
William C. Schulz Vector Identities from Quaternions . . . 271--273
Anonymous Calendar of Future Meetings . . . . . . 273--274
Erwin Just Problems . . . . . . . . . . . . . . . . 274--279
Ross Honsberger Mathematical Gems . . . . . . . . . . . 280--282
Henry L. Alder Harry Merrill Gehman 1898--1981 . . . . 283--284
Pierre J. Malraison Book Reviews . . . . . . . . . . . . . . 285--286
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 286--287
Anonymous Editorial Board . . . . . . . . . . . . ??
Gina Bari Kolata A Profile of Ronald L. Graham . . . . . 290--301
Anonymous Computers & Calculators . . . . . . . . . 301--301
Gary E. Stevens Forward and Backward with Euclid . . . . 302--306
Allan J. Ceasar The Saint Petersburg Paradox and Some
Related Series . . . . . . . . . . . . . 306--308
Betsy Darken Smith Misguided Mathematical Maxim-Makers . . 309--316
Ronald E. Kutz Two Unusual Sequences . . . . . . . . . 316--319
Calvin T. Long How Many Positive Integers Have Nines in
Their Decimal Representations? . . . . . 320--324
Ross Honsberger Mathematical Gems . . . . . . . . . . . 325--329
Warren Page and
R. S. Luthar A Standard Integral Formula . . . . . . 329--330
Joseph A. Gallian An Optimal Football Strategy . . . . . . 330--331
Norman Schaumberger A Classroom Approach to $ x^2 $ + $ y^2
$ + $ z^2 $ = $ w^2 $ . . . . . . . . . 331--332
Michael W. Ecker Must a ``Dud'' Necessarily Be an
Inflection Point? . . . . . . . . . . . 332--333
Eddie Boyd, Jr. Constructing ``Different'' Examples for
Beginning Abstract Algebra Students . . 333--334
Warren Page and
Leo Chosid Synthetic Division Shortened . . . . . . 334--336
Erwin Just Problems . . . . . . . . . . . . . . . . 336--347
Anonymous Calendar of Future Meetings . . . . . . 347--348
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 348--349
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers and
Lynn Arthur Steen A Conversation with Don Knuth: Part 1 2--18
Robert Hanson Integer Matrices Whose Inverses Contain
Only Integers . . . . . . . . . . . . . 18--21
A. Wilansky Smith Numbers . . . . . . . . . . . . . 21--21
Sheldon P. Gordon Computers and Calculators . . . . . . . 22--27
David J. Thuente Chain Letters: a Poor Investment Unless
\ldots . . . . . . . . . . . . . . . . . 28--35
Ross Honsberger Mathematical Gems . . . . . . . . . . . 36--44
V. N. Murty and
B. H. Bissinger The Law of Succession and Bayes' Rule 44--51
Jane T. Grossman and
Michael P. Grossman Dimple or No Dimple . . . . . . . . . . 52--55
Gareth Williams Mathematics In Archaeology . . . . . . . 56--58
David Y. Hsu Prc A Simple Divisibility Algorithm . . . . 58--59
Allan J. Kroopnick A Note on Parallel Curves . . . . . . . 59--61
Norman Schaumberger A Classroom Approach to Pythagorean
Triples . . . . . . . . . . . . . . . . 61--63
Arthur C. Segal A Note on the Surface of a Sphere . . . 63--64
Erwin Just Problems . . . . . . . . . . . . . . . . 64--71
Henry S. Tropp Book Reviews . . . . . . . . . . . . . . 72--73
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 74--76
Anonymous Editorial Board . . . . . . . . . . . . ??
Douglas R. Hofstadter Analogies and Metaphors to Explain
Gödel's Theorem . . . . . . . . . . . . . 98--114
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 114--164
Rudy Rucker A Machine as Smart as God . . . . . . . 115--121
Jean H. Bevis and
Jan L. Boal Computers and Calculators . . . . . . . 122--127
Donald J. Albers and
Lynn Arthur Steen A Conversation with Don Knuth: Part 2 128--141
Raymond Smullyan The Asylum of Doctor Tarr and Professor
Fether . . . . . . . . . . . . . . . . . 142--145
Martin Gardner Who is Raymond Smullyan? . . . . . . . . 146--146
Erwin Just Problems . . . . . . . . . . . . . . . . 147--154
Warren Page and
Allen J. Schwenk Selection of a Fair Currency Exchange
Rate . . . . . . . . . . . . . . . . . . 154--155
Kong-Ming Chong Differential Operators Applied to
Integration . . . . . . . . . . . . . . 155--157
Branislav Marti\'c Remark on an Elementary Gem Concerning $
\Pi (n) $ . . . . . . . . . . . . . . . 158--159
Norman Schaumberger Still Another Proof of the
Arithmetic--Geometric Mean Inequality 159--160
M. Perisastry and
V. N. Murty Bounds for the Ratio of the Arithmetic
Mean to the Geometric Mean . . . . . . . 160--161
William G. Chinn Two New Mathematics Research Institutes 162--163
Anonymous Editorial Board . . . . . . . . . . . . ??
Tom Davis Teaching Mathematics with Rubik's Cube 178--185
Katharine O'Brien Aftermath . . . . . . . . . . . . . . . 185--185
Herb Holden Chords of the Parabola . . . . . . . . . 186--190
Ralph Boas Power Series for Practical Purposes . . 191--195
Warren Page and
William A. Leonard Intuition Out to Sea . . . . . . . . . . 195--196
David Y. Hsu Sums of Powers of the First $n$ Integers 196--197
M. G. Monzingo A Visual Interpretation of Independent
Events . . . . . . . . . . . . . . . . . 197--198
Bill Bompart An Alternate Method for Solving Radical
Equations . . . . . . . . . . . . . . . 198--199
Franklin Kemp Infinite Series Flow Chart for $ \sum
a_n^\dagger $ . . . . . . . . . . . . . 199--199
Alice W. Essary Rectangular Aids for Polar Graphs . . . 200--203
Peter Renz How Good a Picture Do You Need? . . . . 204--205
Erwin Just Problems . . . . . . . . . . . . . . . . 206--212
Raymond Smullyan The Asylum of Doctor Tarr and Professor
Fether: Solutions . . . . . . . . . . . 213--217
Paul J. Campbell Book Reviews . . . . . . . . . . . . . . 217--218
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 219--220
Ronald M. Davis The Signpost: News & Commentary . . . . . 221--222
James Baldwin News From Amatyc . . . . . . . . . . . . 222--222
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers Paul Halmos: Maverick Mathologist . . . 226--242
P. R. Halmos The Thrills of Abstraction . . . . . . . 243--251
Michael Gilpin Computer and Calculators . . . . . . . . 252--259
Ross Honsberger Mathematical Gems . . . . . . . . . . . 260--265
Thomas E. Elsner Taxes on Taxes . . . . . . . . . . . . . 266--269
Warren Page and
K. R. S. Sastry An Equal Ratio Property for Convex
Polygons . . . . . . . . . . . . . . . . 269--270
Arthur C. Segal Motivating $e$ by Calculator . . . . . . 271--271
Homer W. Austin Probability Solution to a Limit Problem 272--272
F. Lee Cook A Simple Explicit Formula for the
Bernoulli Numbers . . . . . . . . . . . 273--274
Norman Schaumberger The Derivative of $ \Arctan x $ . . . . 274--276
Erwin Just Problems . . . . . . . . . . . . . . . . 276--283
Ronald M. Davis The Signpost: News And Commentary . . . 283--284
James Baldwin News From Amatyc . . . . . . . . . . . . 285--285
G. L. Alexanderson and
J. E. Householder Book Reviews . . . . . . . . . . . . . . 286--288
Anonymous Editorial Board . . . . . . . . . . . . ??
Richard K. Guy John Horton Conway: Mathematical Magus 290--299
Richard Bronson Computers & Calculators . . . . . . . . . 300--310
John D. Neff Dice Tossing and Pascal's Triangle . . . 311--314
Warren Page and
V. N. Murty Nearness Relations Among Measures of
Central Tendency and Dispersion: Part 1 315--327
Warren Page and
Michael W. Ecker The Sums of Zeros of Polynomial
Derivatives . . . . . . . . . . . . . . 328--329
Norman Schaumberger and
Norman Schaumberger The Euler Line: a Vector Approach . . . 329--331
Lee Badger A Nonlogarithmic Proof That $ (1 + 1 /
n)^n \to e $ . . . . . . . . . . . . . . 331--332
Erwin Just Problems . . . . . . . . . . . . . . . . 333--342
Ronald M. Davis The Signpost: News Commentary . . . . . 343--346
Anonymous Editorial Board . . . . . . . . . . . . ??
Ross Honsberger Mathematical Gems . . . . . . . . . . . 2--8
Warren Page and
V. N. Murty Nearness Relations Among Measures of
Central Tendency and Dispersion: Part 2 8--17
Lynn Arthur Steen John G. Kemeny: Computing Pioneer . . . 18--35
J. L. Brenner Labeling of Graphs . . . . . . . . . . . 36--41
Larry King The $ \epsilon $--$ \delta $ Connection 42--47
Ali R. Amir-Moéz Isomorphisms on Magic Squares . . . . . 48--51
Lyle Cook and
James McWilliam Computers & Calculators . . . . . . . . . 52--54
Warren Page and
Dan Kalman Sum Formulas for Sine and Cosine . . . . 55--56
Donald D. Elliott A Prime-Generating Function . . . . . . 57--57
W. L. Perry A Bifurcation Problem In First Semester
Calculus . . . . . . . . . . . . . . . . 57--60
J. E. Nymann An Alternative for Partial Fractions
(part of the time) . . . . . . . . . . . 60--61
Anonymous Editorial Board . . . . . . . . . . . . ??
Philip J. Davis The Thread . . . . . . . . . . . . . . . 98--104
Michael W. Ecker The Alluring Lore of Cyclic Numbers . . 105--109
Padmini T. Joshi Efficient Techniques for Partial
Fractions . . . . . . . . . . . . . . . 110--118
Arthur C. Segal Closed-Form Formulas for Quasi-Geometric
Series . . . . . . . . . . . . . . . . . 118--122
Harry Hutchins License Numbers and Divisibility Rules 122--125
G. L. Alexanderson and
Carroll Wilde A Conversation with Garrett Birkhoff . . 126--145
Stephen B. Maurer Some Unusual Locus Problems . . . . . . 146--153
Ross Honsberger Mathematical Gems . . . . . . . . . . . 154--158
Michael W. Chamberlain Computers & Calculators . . . . . . . . . 159--164
Warren Page and
David Y. Hsu Minimization Based on the Greatest
Common Divisor . . . . . . . . . . . . . 164--166
Glen Peterson Approximation to an Angle Trisection . . 166--167
Joseph Wiener Evaluating Integrals by Differentiation 168--169
Richard C. Bollinger How to Make a Bank Shot . . . . . . . . 169--170
Warren Page Interfractile Ranges . . . . . . . . . . 170--172
Anonymous Problems . . . . . . . . . . . . . . . . 172--178
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 179--181
Anonymous Editorial Board . . . . . . . . . . . . ??
Ray C. Shiflett and
Harris S. Shultz When Does A Square Give Maximum Area? 194--196
John D. Neff Imbedding the Metric . . . . . . . . . . 197--202
Sylvan Burgstahler A Generalization of Cramer's Rule . . . 203--205
Joan R. Leitzel Toward a Common Understanding of the
Content of College Preparatory
Mathematics . . . . . . . . . . . . . . 206--209
Stephen B. Maurer An Interview with Albert W. Tucker . . . 210--224
Albert W. Tucker Solomon Lefschetz: a Reminiscence . . . 225--227
A. W. Tucker and
Philip D. Straffin, Jr. The Mathematics of Tucker: a Sampler . . 228--232
David R. Stoutemyer Computers & Calculators . . . . . . . . . 233--239
Ruma Falk and
Maya Bar-Hillel Probabilistic Dependence Between Events 240--247
Michael R. Latina Some Maximal Rectangles and the
Realities of Applied Mathematics . . . . 248--252
Lenny K. Jones Sequences, Series, and Pascal's Triangle 253--256
Bruce Sommer and
Norman Schaumberger Evaluating f sec x dx and f sec$^3$ x
dx . . . . . . . . . . . . . . . . . . . 256--257
Phyllis Lefton Congruences of Cyclotomic Polynomials 257--258
Robert Bumcrot Exactly $n$-Times Differentiable
Functions . . . . . . . . . . . . . . . 258--259
Anonymous Problems . . . . . . . . . . . . . . . . 260--265
Donald J. Albers and
R. P. Boas Book Reviews . . . . . . . . . . . . . . 266--267
Anonymous The Signpost: News & Commentary . . . . . 268--269
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 269--271
Anonymous Editorial Board . . . . . . . . . . . . ??
G. L. Alexanderson A Glimpse at the Pólya Picture Album . . 274--294
Richard J. Trudeau How Big Is a Point? . . . . . . . . . . 295--300
Charles G. Moore The Construction of Integral Cevians . . 301--308
John Scheding SSD Persistence: a Mathematical System
for Student Investigation . . . . . . . 309--312
Ali R. Amir-Moéz Roots of Polynomials and Loci . . . . . 313--317
Pansy Waycaster Brunson A Classroom Experiment Involving Basic
Mathematics and Women . . . . . . . . . 318--321
David Cusick Computers & Calculators: a Logarithm
Algorithm for Four-Function Calculators 322--324
Donald L. Muench and
Gerald Wildenberg A Logarithm Algorithm for a
Five-Function Calculator . . . . . . . . 324--326
J. N. Boyd and
P. N. Raychowdhury A Computational Approach to Logical
Statements . . . . . . . . . . . . . . . 326--328
John F. Lucas Paths and Pascal Numbers . . . . . . . . 329--341
Ralph P. Boas The Versed of Boas . . . . . . . . . . . 342--344
Philip G. Buckhiester Blackjack with $n$ Decks . . . . . . . . 345--346
Phillip Schultz An Algebraic Approach to Partial
Fractions . . . . . . . . . . . . . . . 346--348
J. N. Boyd and
P. N. Raychowdhury An Application of Convex Coordinates . . 348--349
Myren Krom On Sums of Powers of Natural Numbers . . 349--351
Norman Schaumberger Instant Hindsight! . . . . . . . . . . . 351--351
Anonymous Problems . . . . . . . . . . . . . . . . 352--359
Clifford H. Wagner Uncertainty in Science and Statistics 360--363
Peter A. Lindstrom Telegraphic Reviews . . . . . . . . . . 363--364
G. L. Alexanderson Book Reviews . . . . . . . . . . . . . . 365--366
Anonymous The Signpost: News & Commentary . . . . . 366--367
Anonymous Editorial Board . . . . . . . . . . . . ??
William G. Chinn and
John B. Lewis Shiing-shen Chern A Man and His Times 370--376
Paul T. Mielke A Tiling of the Plane with Triangles . . 377--381
Calvin T. Long On the Radii of the Inscribed and
Escribed Circles of Right Triangles ---
a Second Look . . . . . . . . . . . . . 382--389
Herman Goldstine Faster than von Neumann? . . . . . . . . 389--389
Byron L. McAllister Products of Sets of Complex Numbers . . 390--397
Nira Hativa What Makes Mathematics Lessons Easy to
Follow, Understand, and Remember? . . . 398--406
Michael Tennor The Address Problem . . . . . . . . . . 407--415
Lester H. Lange Book Reviews . . . . . . . . . . . . . . 415--415
Thomas Kersten Computer Simulations to Clarify Key
Ideas of Statistics . . . . . . . . . . 416--421
Dorothy Goldberg Integrating Writing into the Mathematics
Curriculum . . . . . . . . . . . . . . . 421--424
Robert R. Christian Another Way to Introduce Natural
Logarithms and $e$ . . . . . . . . . . . 424--426
Leon Wejntrob Approximation of Square Roots . . . . . 427--431
Frank Burk Mean Inequalities . . . . . . . . . . . 431--434
L. Whitt and
K. Wilk and
Daniel H. Wagner Antisubmarine Warfare: Passive vs.
Active Sonar . . . . . . . . . . . . . . 434--435
Alden R. Partridge Ellipses From a Circular and Spherical
Point of View . . . . . . . . . . . . . 436--438
Anonymous Problems . . . . . . . . . . . . . . . . 438--438
Anonymous Editorial Board . . . . . . . . . . . . ??
Warren Page An Interview with Herbert Robbins . . . 2--24
Herbert Robbins Some Breakthroughs in Statistical
Methodology . . . . . . . . . . . . . . 25--29
Kay Dundas To Build a Better Box . . . . . . . . . 30--36
Victor A. Belfi Convexity in Elementary Calculus: Some
Geometric Equivalences . . . . . . . . . 37--41
Dan Kalman Basic Null Space Calculations . . . . . 42--47
Mou-Liang Kung and
George C. Harrison Is the Venn Diagram Good Enough? . . . . 48--50
Robert J. Bumcrot Some Subtleties in L'Hôpital's Rule . . . 51--52
Jonathan W. Lewin An Analytic Approach to the Euler Line 52--53
Syed Asadulla Digital Roots of Mersenne Primes and
Even Perfect Numbers . . . . . . . . . . 53--54
R. S. Luthar Integer-Sided Triangles with One Angle
Twice Another . . . . . . . . . . . . . 55--56
Sylvan Burgstahler An Alternative for Certain Partial
Fractions . . . . . . . . . . . . . . . 57--58
John C. Huber and
Joseph Wiener Deriving the Equations of the Ellipse
and Hyperbola . . . . . . . . . . . . . 58--59
Vedula N. Murty On the Mean and Standard Deviation of a
Random Sample . . . . . . . . . . . . . 60--63
Sheldon P. Gordon Evaluating e$^x$ Using Limits . . . . . 63--65
Anonymous Software Reviews . . . . . . . . . . . . 65--67
Anonymous Problems . . . . . . . . . . . . . . . . 68--74
Anonymous Guidelines for Authors . . . . . . . . . 75--75
Robert V. Hogg Media Highlights . . . . . . . . . . . . 76--84
Anonymous Editorial Board . . . . . . . . . . . . ??
Anthony Barcellos The Fractal Geometry of Mandelbrot . . . 98--114
Beno\^\it B. Mandelbrot Additional Perspectives on Fractals . . 115--119
Stephen H. Friedberg The Distribution of First Digits . . . . 120--125
Marshall Fraser The Grazing Goat in $n$ Dimensions . . . 126--134
Larry Hoehn A Geometrical Interpretation of the
Weighted Mean . . . . . . . . . . . . . 135--139
Michael K. Brozinsky Reflection Property of the Ellipse and
the Hyperbola . . . . . . . . . . . . . 140--142
William Moser A Sequel to ``Another Way of Looking at
$ n! $'' . . . . . . . . . . . . . . . . 142--143
Norman Schaumberger The Derivatives of $ \Sin x $ and $ \Cos
x $ . . . . . . . . . . . . . . . . . . 143--145
Curtis Cooper Application of a Generalized Fibonacci
Sequence . . . . . . . . . . . . . . . . 145--147
Deane E. Arganbright The Electronic Spreadsheet and
Mathematical Algorithms . . . . . . . . 148--157
Curt Suplee Zork, RAMS and the Curse of Ra: Computo,
ergo sum . . . . . . . . . . . . . . . . 158--159
Richard C. Detmer and
L. Carl Leinbach Software Reviews . . . . . . . . . . . . 159--162
Anonymous Problems . . . . . . . . . . . . . . . . 163--169
Don Chakerian Media Highlights . . . . . . . . . . . . 170--177
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers and
Michael J. Thibodeaux A Conversation with Henry Pollak . . . . 194--217
Jean Pedersen and
George Pólya On Problems with Solutions Attainable in
More Than One Way . . . . . . . . . . . 218--228
Janet Bellcourt Pomeranz The Dice Problem-Then and Now . . . . . 229--237
Branko Grünbaum The Construction of Venn Diagrams . . . 238--247
Alec Norton and
Benjamin Lotto Complex Roots Made Visible . . . . . . . 248--249
Norman Schaumberger Another Look at $ x^{1 / x} $ . . . . . 249--250
Karl David An Odd Induction Proof . . . . . . . . . 251--251
David E. Dobbs Proving Heron's Formula Tangentially . . 252--253
Michael Henry and
G. E. Trapp, Jr. Income Tax Averaging and Convexity . . . 253--255
Robert Geist How to Live to Be 100 . . . . . . . . . 256--263
Anonymous Software Reviews . . . . . . . . . . . . 263--265
Anonymous Problems . . . . . . . . . . . . . . . . 266--273
Peter J. Hilton Media Highlights . . . . . . . . . . . . 274--283
Anonymous Editorial Board . . . . . . . . . . . . ??
Calvin Long Pascal's Triangle, Difference Tables and
Arithmetic Sequences of Order $N$ . . . 290--298
W. G. Leavitt Repeating Decimals . . . . . . . . . . . 299--308
Robert E. Kennedy and
Curtis N. Cooper On the Natural Density of the Niven
Numbers . . . . . . . . . . . . . . . . 309--312
Duane W. DeTemple Geometric Procedures for Graphing the
General Quadratic Equation . . . . . . . 313--323
Joseph Wiener Pythagorean Systems of Numbers . . . . . 324--326
Man-Keung Siu On the Sphere and Cylinder . . . . . . . 326--328
Abdus Sattar Gazdar Distance From a Point to a Line . . . . 328--329
Dan Kalman The Maximum and Minimum of Two Numbers
Using the Quadratic Formula . . . . . . 329--330
Robert Schmidt and
Robert Lacher Probabilistic Repeatability Among Some
Irrationals . . . . . . . . . . . . . . 330--332
R. A. Mureika and
R. D. Small An Almost Correct Series . . . . . . . . 334--338
Allan J. Ceasar A Monte Carlo Simulation Related to the
St. Petersburg Paradox . . . . . . . . . 339--342
Tom Moore Software Reviews . . . . . . . . . . . . 343--344
Anonymous Problems . . . . . . . . . . . . . . . . 346--353
Ann Watkins Media Highlights . . . . . . . . . . . . 354--361
Anonymous Editorial Board . . . . . . . . . . . . ??
Warren Page Forum . . . . . . . . . . . . . . . . . 370--370
Anthony Ralston Will Discrete Mathematics Surpass
Calculus in Importance? . . . . . . . . 371--373
Saunders MacLane Calculus is a Discipline \ldots . . . . 373--373
Daniel H. Wagner Calculus versus Discrete Mathematics in
OR Applications \ldots . . . . . . . . . 374--375
Peter J. Hilton The Need for Coherence and Unity \ldots 375--375
R. L. Woodriff A Distinctly Discrete Indiscretion
\ldots . . . . . . . . . . . . . . . . . 376--377
Daniel J. Kleitman Calculus Defended \ldots . . . . . . . . 377--378
Peter D. Lax In Praise of Calculus \ldots . . . . . . 378--380
Anonymous Anthony Ralston's Response . . . . . . . 380--382
Fred S. Roberts The Introductory Mathematics Curriculum:
Misleading, Outdated, and Unfair . . . . 383--385
William F. Lucas Discrete Mathematics Courses Have
Constituents Besides Computer Scientists
\ldots . . . . . . . . . . . . . . . . . 386--388
R. W. Hamming Calculus and Discrete Mathematics \ldots 388--389
David Tall Continuous Mathematics and Discrete
Computing are Complementary, Not
Alternatives \ldots . . . . . . . . . . 389--391
Robert B. Davis It's Not What You Do, It's How You Do It
\ldots . . . . . . . . . . . . . . . . . 391--393
Wade Ellis, Jr. Teaching is Mathematics, too \ldots . . 393--394
Patrick W. Thompson Issues of Content versus Method \ldots 394--395
John Mason A Need for Better Role Models and
Attitudes \ldots . . . . . . . . . . . . 395--396
Richard K. Guy How Can We Lead in an Up-to-Date and
Fair Fashion? \ldots . . . . . . . . . . 396--397
Anonymous Fred Roberts' Response . . . . . . . . . 397--399
James E. Schultz and
William F. Burger An Approach to Problem-Solving Using
Equivalence Classes Modulo $n$ . . . . . 401--405
Tom Brieske Visual Thinking about Rotations and
Reflections . . . . . . . . . . . . . . 406--410
Frank Harary and
Robert W. Robinson Connect-it Games . . . . . . . . . . . . 411--419
David Gauld Approximate Angle Trisection . . . . . . 420--422
Norman Schaumberger Alternate Approaches to Two Familiar
Results . . . . . . . . . . . . . . . . 422--423
Steven Schwartzman The Factorial Triangle and Polynomial
Sequences . . . . . . . . . . . . . . . 424--426
W. Vance Underhill Finding Bounds for Definite Integrals 426--429
William Parsons Right Triangles with Perimeter and Area
Equal . . . . . . . . . . . . . . . . . 429--429
Mark D. Meyerson Return of the Grazing Goat in $n$
Dimensions . . . . . . . . . . . . . . . 430--432
Branko Grünbaum On Venn Diagrams and the Counting of
Regions . . . . . . . . . . . . . . . . 433--435
T. E. Gantner The Computation of Repeating Decimals 436--440
Florence S. Gordon and
Sheldon P. Gordon Mathematical Discovery via Computer
Graphics: Hypocycloids and Epicycloids 440--443
G. Ernest Anderson, Jr. Software Reviews . . . . . . . . . . . . 444--444
Anonymous Problems . . . . . . . . . . . . . . . . 445--451
Stephen B. Maurer Media Highlights . . . . . . . . . . . . 452--460
Anonymous Acknowledgements . . . . . . . . . . . . 460--460
Anonymous Editorial Board . . . . . . . . . . . . ??
Stephen B. Maurer The Algorithmic Way of Life is Best . . 2--5
R. G. Douglas One Needs More than the Algorithmic
Approach . . . . . . . . . . . . . . . . 5--6
Bernhard Korte Algorithmic Mathematics versus Dialectic
Mathematics . . . . . . . . . . . . . . 6--8
Peter Hilton Algorithms are Not Enough . . . . . . . 8--9
Peter Renz The Path to Hell . . . . . . . . . . . . 9--11
Craig Smory\'nski The Need for Abstraction . . . . . . . . 11--12
J. M. Hammersley Three Algorithmic Exercises . . . . . . 12--14
P. R. Halmos Pure Thought is Better Yet . . . . . . . 14--16
George B. Dantzig Stephen Maurer's Response . . . . . . . 17--21
Philip J. Davis What Do I Know? A Study of Mathematical
Self-Awareness . . . . . . . . . . . . . 22--41
Ralph P. Boas Inverse Functions . . . . . . . . . . . 42--47
W. J. Hildebrand Generalized Pythagorean Triples . . . . 48--52
Gino T. Fala Income Averaging Can Increase Your Tax
Liability . . . . . . . . . . . . . . . 53--55
Lee Whitt Medical Cozenage on Fermat's Last
Theorem . . . . . . . . . . . . . . . . 55--56
Frank Buck Behold! The Midpoint Rule is Better Than
the Trapezoidal Rule for Concave
Functions . . . . . . . . . . . . . . . 56--56
Sui-Sun Cheng and
Tzon-Tzer Lu The Bisection Algorithm is Not Linearly
Convergent . . . . . . . . . . . . . . . 56--57
Dan Kalman and
Warren Page Nested Polynomials and Efficient
Exponentiation Algorithms for
Calculators . . . . . . . . . . . . . . 57--60
Anonymous Guidelines for Authors . . . . . . . . . 61--61
Bart Braden Picturing Functions of a Complex
Variable . . . . . . . . . . . . . . . . 63--72
Elliot Tanis Software Reviews . . . . . . . . . . . . 72--73
Anonymous Problems . . . . . . . . . . . . . . . . 74--80
Charles V. Jones Media Highlights . . . . . . . . . . . . 81--86
Anonymous Editorial Board . . . . . . . . . . . . ??
David H. Nash Differential Equations and the Battle of
Trafalgar . . . . . . . . . . . . . . . 98--102
Dan Kalman Rediscovering Taylor's Theorem . . . . . 103--107
Joey Paul The House Number Problem and its
Variations . . . . . . . . . . . . . . . 108--117
Raymond M. Smullyan Satan, Cantor, and Infinity . . . . . . 118--121
Charles G. Moore Constructing the Foci and Directrices of
a Given Ellipse . . . . . . . . . . . . 122--128
B. M. Saler Inverse Hyperbolic Functions as Areas 129--131
Peter A. Lindstrom A Self-contained Derivation of the
Formula $ d / d x (x^r) = r x^{r - 1} $
for Rational $r$ . . . . . . . . . . . . 131--132
David E. Dobbs Average Values and Linear Functions . . 132--135
Fon Brown and
L. O. Cannon and
Joe Elich and
David G. Wright On Rearrangements of the Alternating
Harmonic Series . . . . . . . . . . . . 135--138
James Smith and
Mason Henderson Tetrahedra, Skew Lines, and Volume . . . 138--140
Bruce H. Edwards and
Patricia L. Sharpe III-Conditioning: a Constant Surprise in
Computational Mathematics . . . . . . . 141--148
Jerry A. Roberts Accurate Computation of Variance . . . . 149--150
James A. Deddens and
Marjorie A. Fitting Software Reviews . . . . . . . . . . . . 151--152
Anonymous Problems . . . . . . . . . . . . . . . . 153--161
H. S. M. Coxeter and
R. P. Boas Media Highlights . . . . . . . . . . . . 162--171
Anonymous Editorial Board . . . . . . . . . . . . ??
Jean Pedersen and
Peter Ross Testing Understanding and Understanding
Testing . . . . . . . . . . . . . . . . 178--185
S. C. Althoen and
J. F. Weidner Related Rates and the Speed of Light . . 186--189
Robert Hanson Self-Inverse Integer Matrices . . . . . 190--198
Dan Kalman Geometrically Asymptotic Curves . . . . 199--206
Roland H. Eddy Behold! The Arithmetic--Geometric Mean
Inequality . . . . . . . . . . . . . . . 208--208
Thomas R. Knapp Instances of Simpson's Paradox . . . . . 209--211
Norman Schaumberger Approximating Solutions for Exponential
Equations . . . . . . . . . . . . . . . 211--212
Vedula N. Murty and
James F. McCrory A General Method of Deriving the
Auxiliary Equation for Cauchy-Euler
Equations . . . . . . . . . . . . . . . 212--215
Raymond N. Greenwell Using Minitab in Linear Algebra . . . . 216--218
Jack Bookman and
David Smith and
Donald E. Rossi Software Reviews . . . . . . . . . . . . 218--222
Anonymous Problems . . . . . . . . . . . . . . . . 223--231
D. Bushaw and
Philip Cheifetz Media Highlights . . . . . . . . . . . . 233--247
Anonymous Editorial Board . . . . . . . . . . . . ??
James L. Kepner On the Probability that the Better Team
Wins the World Series . . . . . . . . . 250--256
Floyd Vest Graphing the Complex Roots of a
Quadratic Equation . . . . . . . . . . . 257--261
I. J. Schoenberg On Hypocycloids and their Diameters . . 262--267
Joseph Whittaker A New Divisibility Algorithm . . . . . . 268--276
David C. Buchthal Predetermined Determinants . . . . . . . 277--279
Frank Burk Euler's Constant . . . . . . . . . . . . 279--279
Norman Schaumberger An Instant Proof of $ e^\pi > \pi^e $ . . 280--280
Robert C. Brigham and
Ronald D. Dutton and
Phyllis Z. Chinn and
Frank Harary Realization of Parity Visits in Walking
a Graph . . . . . . . . . . . . . . . . 280--282
André L. Yandl A Note on Integration by Parts . . . . . 282--283
Irl C. Bivens and
L. R. King Relating Differentiability and Uniform
Continuity . . . . . . . . . . . . . . . 283--283
William Miller Both a Borrower and a Lender Be . . . . 284--284
Will Watkins Vectors in a LOGO Learning Environment 286--300
Roy E. Myers and
Carol M. Smith and
Marjorie A. Fitting and
Henry Africk Software Reviews . . . . . . . . . . . . 301--303
Anonymous Problems . . . . . . . . . . . . . . . . 304--311
James J. Kaput Media Highlights . . . . . . . . . . . . 312--322
Anonymous Editorial Board . . . . . . . . . . . . ??
Nura D. Turner A Historical Sketch of Olympiads: U.S.A.
and International . . . . . . . . . . . 330--335
Warren Page An Interview with the 1985 USA Team to
the International Mathematical Olympiad 336--360
Cecil Rousseau and
Gregg Patruno The International Mathematical Olympiad
Training Session . . . . . . . . . . . . 362--365
Nura D. Turner A Follow-up on the USAMO Winners . . . . 366--368
Loren C. Larson A Discrete Look at 1 + 2 + \ldots + $n$ 369--382
Sherman Stein Routine Problems . . . . . . . . . . . . 383--385
Philip D. Straffin, Jr. Three Person Winner-Take-All Games with
McCarthy's Revenge Rule . . . . . . . . 386--394
John D. Baildon Arithmetic Progressions and the Consumer 395--397
Norman Schaumberger More Applications of the Mean Value
Theorem . . . . . . . . . . . . . . . . 397--398
Larry E. Knop Cantor's Disappearing Table . . . . . . 398--399
Joseph Wiener Bernoulli's Inequality and the Number
$e$ . . . . . . . . . . . . . . . . . . 399--400
R. Rozen and
A. Sofo Area of a Parabolic Region . . . . . . . 400--402
Gerard Kiernan Computing Large Factorials . . . . . . . 403--412
Cynthia Schmalzried and
James A. Deddens and
Thomas J. Carter Software Reviews . . . . . . . . . . . . 413--415
Anonymous Problems . . . . . . . . . . . . . . . . 416--424
Thomas P. Faase and
G. L. Alexanderson Media Highlights . . . . . . . . . . . . 425--432
P. J. O'Halloran Josephine Dianne Edwards . . . . . . . . 433--433
Anonymous Acknowledgements . . . . . . . . . . . . 434--434
Anonymous Editorial Board . . . . . . . . . . . . ??
Constance Reid The Autobiography of Julia Robinson . . 2--21
James K. Bidwell A Babylonian Geometrical Algebra . . . . 22--31
Warren Page Mathematical Competition in Modeling . . 32--33
Michael Caulfield and
John Kent and
Daniel McCaffrey Harvesting a Grizzly Bear Population . . 34--46
David Cole and
Loren Haarsma and
Jack Snoeyink The Problem of Managing a Strategic
Reserve . . . . . . . . . . . . . . . . 48--60
Kyle D. Wallace Cyclic Diversions . . . . . . . . . . . 61--65
Paul Schaefer Sums of Rearranged Series . . . . . . . 66--70
Joseph Wiener An Algebraic Approach to Partial
Fractions . . . . . . . . . . . . . . . 71--72
William C. Schulz An Alternate Proof of the Vector Triple
Product Formula . . . . . . . . . . . . 73--74
Florence S. Gordon A Nonstandard Solution to A Standard
Problem . . . . . . . . . . . . . . . . 74--74
Frank Burk Some Interesting Consequences of a
Hyperbolic Inequality . . . . . . . . . 75--76
Curtis Cooper Trees and Tennis Rankings . . . . . . . 76--78
Howard Lewis Penn Computer Graphics for the Vibrating
String . . . . . . . . . . . . . . . . . 79--89
L. Carl Leinbach and
Rosemary Hirschfelder Software Reviews . . . . . . . . . . . . 90--91
Anonymous Problems . . . . . . . . . . . . . . . . 92--99
Philip J. Davis Media Highlights . . . . . . . . . . . . 101--109
Anonymous Guidelines for Authors . . . . . . . . . 110--110
Anonymous Editorial Board . . . . . . . . . . . . ??
Sydney C. K. Chu and
Man-Keung Siu How Far Can You Stick Out Your Neck? . . 122--132
Irl C. Bivens What a Tangent Line is When it isn't a
Limit . . . . . . . . . . . . . . . . . 133--143
John F. Putz The Pascal Polytope: an Extension of
Pascal's Triangle to $N$ Dimensions . . 144--155
Ruma Falk Of Probabilistic Knights and Knaves . . 156--164
J. Richard Morris Counterexamples to a Comparison Test for
Alternating Series . . . . . . . . . . . 165--166
Russell Euler A Note on Differentiation . . . . . . . 166--167
Dan Kalman Angling for Pythagorean Triples . . . . 167--168
Alvin Tirman Geometric Parametrization of Pythagorean
Triples . . . . . . . . . . . . . . . . 168--168
Stewart Venit and
Wayne Bishop Classifying Row-reduced Echelon Matrices 169--170
Frank Burk and
Sudhir K. Goel and
Dennis M. Rodriguez Using Riemann Sums in Evaluating a
Familiar Limit . . . . . . . . . . . . . 170--171
Michael E. Frantz Interactive Graphics for Multivariable
Calculus . . . . . . . . . . . . . . . . 172--181
John Riegsecker and
Judith L. Clarke and
Carol M. Smith Software Reviews . . . . . . . . . . . . 182--183
Anonymous Problems . . . . . . . . . . . . . . . . 184--189
I. J. Schoenberg Media Highlights . . . . . . . . . . . . 190--199
Anonymous Editorial Board . . . . . . . . . . . . ??
Sharon Kunoff and
Sylvia Pines Teaching Elementary Probability Through
its History . . . . . . . . . . . . . . 210--219
Herbert R. Bailey How to Balance a Yardstick on an Apple 220--225
Richard L. Francis From None to Infinity: Challenging
Problems in Cardinality Classification 226--230
Charles H. Jepsen Coloring Points in the Unit Square . . . 231--237
Leroy F. Meyers Three Ways to Maximize the Area of an
Inscribed Quadrilateral . . . . . . . . 238--239
S. A. Patil and
V. R. R. Uppuluri The Distribution of First $j$ Digits . . 240--243
Robert J. Bumcrot Irrationality Made Easy . . . . . . . . 243--244
Norman Schaumberger The Derivatives of $ \Arcsec x $, $
\Arctan x $, and $ \Tan x $ . . . . . . 244--246
Soo Tang Tan A Case of True Interest . . . . . . . . 247--248
Anonymous Problems . . . . . . . . . . . . . . . . 249--254
R. S. Cunningham and
David A. Smith A Mathematics Software Database . . . . 255--266
Ivan Niven Media Highlights . . . . . . . . . . . . 267--275
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers and
Constance Reid An Interview with George B. Dantzig: The
Father of Linear Programming . . . . . . 292--314
Robert L. Hocking and
Neil C. Schwertman An Extension of the Birthday Problem to
Exactly $k$ Matches . . . . . . . . . . 315--321
Robert A. Cicenia Picturing Infinite Values . . . . . . . 322--325
Bart Braden The Surveyor's Area Formula . . . . . . 326--337
Fouad Nakhli Behold! The Vertex Angles of a Star Sum
to $ 180^\circ $ . . . . . . . . . . . . 338--338
Norman Schaumberger Three Familiar Formulas for $ \pi $ via
Geometry . . . . . . . . . . . . . . . . 339--339
A. Tan A Geometric Interpretation of Simpson's
Paradox . . . . . . . . . . . . . . . . 340--341
R. P. Boas Does ``holds water'' Hold Water? . . . . 341--341
Robert C. Moore Doubling: Real, Complex, Quaternion, and
Beyond \ldots Well, Maybe . . . . . . . 342--343
Edward J. LeCuyer, Jr. Teaching Mathematics Using APL . . . . . 344--358
Judith R. Brown and
Robert A. Beezer Software Reviews . . . . . . . . . . . . 358--359
Anonymous Problems . . . . . . . . . . . . . . . . 360--365
David Wheeler Media Highlights . . . . . . . . . . . . 366--375
Anonymous Editorial Board . . . . . . . . . . . . ??
Harley Flanders On Polynomial Matrix Equations . . . . . 388--391
Larry Cannon Geometry of the Rational Plane . . . . . 392--402
Robert S. Smith Rolle over Lagrange-Another Shot at the
Mean Value Theorem . . . . . . . . . . . 403--406
Joel Spencer Combinatorics by Coin Flipping . . . . . 407--412
Chris Freiling The Change of Base Formula for
Logarithms . . . . . . . . . . . . . . . 413--413
Frances W. Lewis Defining Area in Polar Coordinates . . . 414--416
Norman Schaumberger Another Approach to a Class of Slowly
Diverging Series . . . . . . . . . . . . 417--417
Zalman P. Usiskin A Pretrigonometry Proof of the
Reflection Property of the Ellipse . . . 418--418
Frank Burk Numerical Integration via Integration by
Parts . . . . . . . . . . . . . . . . . 418--422
Michael Hardy Behold! The Pythagorean Theorem via Mean
Proportions . . . . . . . . . . . . . . 422--422
Don Small and
John Hosack and
Kenneth Lane Computer Algebra Systems in
Undergraduate Instruction . . . . . . . 423--433
John M. Hosack Software Reviews . . . . . . . . . . . . 434--441
Anonymous Problems . . . . . . . . . . . . . . . . 442--449
Anonymous Media Highlights . . . . . . . . . . . . 450--456
Anonymous Editorial Board . . . . . . . . . . . . ??
Dennis Luciano and
Gordon Prichett Cryptology: From Caesar Ciphers to
Public-key Cryptosystems . . . . . . . . 2--17
William Dunham The Bernoullis and the Harmonic Series 18--23
Fred Buckley Facility Location Problems . . . . . . . 24--32
Anonymous Guidelines for Authors . . . . . . . . . 33--33
Jeff Cronk and
Duff Howell and
Keith Saints Positioning of Emergency Facilities in
an Obstructed Traffic Grid . . . . . . . 34--43
Arthur C. Segal A Linear Diet Model . . . . . . . . . . 44--45
Kurt W. Reimann Annuities as Areas . . . . . . . . . . . 45--47
Clyde Dubbs and
David Siegel Computing Determinants . . . . . . . . . 48--50
John Rosendahl Comparing $ B^A $ and $ A^B $ for $ A > B
$ . . . . . . . . . . . . . . . . . . . 50--50
Frank Burk $ \pi / 4 $ and $ \ln 2 $ Recursively 51--51
Ayoub B. Ayoub Behold! The Graphs of $f$ and $ f^{-1}$,
are Reflections About the Line $ y = x$ 52--52
Harley Flanders Algorithm of The Bi-Month . . . . . . . 53--57
Judah L. Schwartz and
Michal Yerushalmy The Geometric Supposer: an Intellectual
Prosthesis for Making Conjectures . . . 58--65
Dan Kunkle and
L. Carl Leinbach and
Judith R. Brown and
Thomas J. Abram and
Carol M. Smith Software Reviews . . . . . . . . . . . . 66--68
Anonymous Problems . . . . . . . . . . . . . . . . 69--77
Ross Honsberger Media Highlights . . . . . . . . . . . . 78--85
Anonymous Editorial Board . . . . . . . . . . . . ??
Patricia C. Kenschaft Charlotte Angas Scott, 1858--1931 . . . 98--110
Robert E. Kennedy and
Curtis N. Cooper Bach, 5465, and Upside-Down Numbers . . 111--115
W. D. Wallis One-Factorizations of Graphs: Tournament
Applications . . . . . . . . . . . . . . 116--123
Jeanne L. Agnew and
James R. Choike Transitions . . . . . . . . . . . . . . 124--133
Robert K. Tamaki Equalizing a Two-Person Alternation Game 134--135
Dan Kalman Cramer's Rule via Selective Annihilation 136--137
Roger C. Alperin Heron's Area Formula . . . . . . . . . . 137--138
Barry A. Cipra The Derivatives of the Sine and Cosine
Functions . . . . . . . . . . . . . . . 139--141
Edward M. Harris Behold! Sums of $ \Arctan $ . . . . . . 141--141
Clifford H. Wagner Enhancing the Value of Graphics Programs 142--152
Harley Flanders Algorithm of The Bi-Month . . . . . . . 153--156
L. Carl Leinbach and
Michael W. Ecker and
Rosemary Hirschfelder and
Sheryl E. Edwards Software Reviews . . . . . . . . . . . . 157--159
Anonymous Problems . . . . . . . . . . . . . . . . 160--166
Edward Page Media Highlights . . . . . . . . . . . . 167--175
Anonymous Editorial Board . . . . . . . . . . . . ??
J. N. Boyd and
P. N. Raychowdhury Convex Coordinates, Probabilities, and
the Superposition of States . . . . . . 186--194
William Watkins Generating Functions . . . . . . . . . . 195--211
William H. Ruckle A Division Game: How Far Can You Stretch
Mathematical Induction? . . . . . . . . 212--218
John C. Hegarty A Depreciation Model for Calculus
Classes . . . . . . . . . . . . . . . . 219--221
Frank Burk Archimedes' Quadrature and Simpson's
Rule . . . . . . . . . . . . . . . . . . 222--223
Norman Schaumberger Extending the Series for In 2 . . . . . 223--225
Herbert Bailey and
Steven C. Althoen and
John Weidner A Surprising Max-Min Result . . . . . . 225--229
Harley Flanders Algorithm of The Bi-Month . . . . . . . 230--235
Franklin Demana and
Bert Waits Problem Solving Using Microcomputers . . 236--241
R. S. Cunningham and
David A. Smith A Mathematics Software Database Update 242--247
Anonymous Problems . . . . . . . . . . . . . . . . 248--252
John W. Berry Media Highlights . . . . . . . . . . . . 253--261
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers and
Constance Reid An Interview with Lipman Bers . . . . . 266--290
LeRoy A. Franklin Bayes' Theorem, Binominal Probabilities,
and Fair Numbers of Peremptory
Challenges in Jury Trials . . . . . . . 291--299
P. R. Scott Equiangular Lattice Polygons and
Semiregular Lattice Polyhedra . . . . . 300--306
Herbert R. Bailey Bat and Superbat . . . . . . . . . . . . 307--314
Wong Ngai Ying Why Is a Restaurant's Business Worse In
the Owner's Eyes Than In the Customers'? 315--316
Warren Page A Rational Approach to Lattice Polygons 316--318
Ali. R. Amir-Moéz Behold! $ (1 \times 2) + (2 \times 3) +
\dots + n \times (n + 1) = (1 / 3)[(n +
1)^3 - (n + 1)] $ . . . . . . . . . . . 318--318
Joseph Wiener A Shorter, More Efficient Proof of $
\lim_{n \to \infty } \sqrt [n]{n!} / n =
e^{-1} $ . . . . . . . . . . . . . . . . 319--319
Isaac J. Schoenberg The Chinese Remainder Problem and
Polynomial Interpolation . . . . . . . . 320--322
Harley Flanders Algorithm of The Bi-Month . . . . . . . 323--327
John Atkins and
Robert Geist Fibonacci Numbers and Computer
Algorithms . . . . . . . . . . . . . . . 328--336
Robert A. Beezer and
Gary Bitter and
Andrew Matchett Software Reviews . . . . . . . . . . . . 337--339
Anonymous Problems . . . . . . . . . . . . . . . . 340--345
Douglas B. McLeod Media Highlights . . . . . . . . . . . . 346--355
Anonymous Editorial Board . . . . . . . . . . . . ??
V. Frederick Rickey Isaac Newton: Man, Myth, and Mathematics 362--389
Roger B. Nelsen and
James E. Schultz The Probability that the ``Sum of the
Rounds'' Equals the ``Round of the Sum'' 390--396
Larry Hoehn Some Properties of Polygons Inside a
Circle . . . . . . . . . . . . . . . . . 397--401
Douglas L. Cashing Is the Distributive Property Redundant? 402--403
David A. Smith Newton's $n$-th Root Method Without
Derivatives . . . . . . . . . . . . . . 403--406
Michael Carchidi Two Simple Recursive Formulas for
Summing 1 $^k$ + 2 $^k$ + 3 $^k$
+ \ldots + \em n$^k$ . . . . . . . . . 406--409
A. R. Amir-Moéz and
Jean Pedersen A Simple Proof of Series Convergence . . 410--410
Joseph F. Aieta Powers and Roots by Recursion . . . . . 411--416
Harley Flanders and
J. Sutherland Frame Algorithm of The Bi-Month . . . . . . . 417--421
Raymond Greenwell and
Carol M. Smith and
Eugene A. Herman Software Reviews . . . . . . . . . . . . 422--424
Anonymous Problems . . . . . . . . . . . . . . . . 425--432
L. C. Moore and
David A. Smith Media Highlights . . . . . . . . . . . . 433--442
Anonymous Editorial Board . . . . . . . . . . . . ??
Warren Page and
David S. Moore Should Mathematicians Teach Statistics? 2--7
A. Blanton Godfrey Should Mathematicians Teach Statistics?
\ldots . . . . . . . . . . . . . . . . . 8--10
Judith Tanur No! But Who Should Teach Statistics?
\ldots . . . . . . . . . . . . . . . . . 11--12
R. Gnanadesikan and
J. R. Kettenring Statistics Teachers Need Experience With
Data \ldots . . . . . . . . . . . . . . 12--14
Barbara A. Bailar The Mathematicians' Statistics Has a
Subsidiary Role \ldots . . . . . . . . . 14--15
Frederick Mosteller Growth and Advances In Statistics . . . 15--16
Gudmund R. Iversen Statistician, Examine Thyself . . . . . 16--18
John E. Freund It's Not ``By Whom,'' But Rather ``How''
\ldots . . . . . . . . . . . . . . . . . 18--20
Henry L. Alder The Need for Good Teaching of Statistics
\ldots . . . . . . . . . . . . . . . . . 20--21
David L. Hanson Let the Experts Teach and Judge \ldots 21--23
Michael Reed Who Teaches What to Whom? . . . . . . . 24--25
Gerald J. Hahn What Should the Introductory Statistics
Course Contain? \ldots . . . . . . . . . 26--29
Ronald D. Snee Mathematics Is Only One Tool That
Statisticians Use \ldots . . . . . . . . 30--32
Anonymous David Moore's Response \ldots . . . . . 32--34
Anonymous The Editor's Concluding Remarks . . . . 34--35
Gary Chartrand and
Paul Erd\Hos and
Ortrud R. Oellermann How to Define an Irregular Graph . . . . 36--42
James A. Uetrecht A Clamped Simpson's Rule . . . . . . . . 43--52
William Staton On Partitioning a Real Number . . . . . 53--54
Roger B. Nelsen The Relationship Between Hyperbolic and
Exponential Functions . . . . . . . . . 54--56
Norman Schaumberger Another Proof of the Inequality Between
Power Means . . . . . . . . . . . . . . 56--58
Sidney H. Kung A Nonstandard Approach to Cramer's Rule 59--60
Kendell Hyde Pascal Triangles and Combinations Where
Repetitions Are Allowed . . . . . . . . 60--62
Edward Rozema Why Should We Pivot in Gaussian
Elimination? . . . . . . . . . . . . . . 63--72
Harley Flanders Algorithm of The Bi-Month . . . . . . . 72--78
K. L. Huehn and
Thomas J. Abram and
Stephen Chang Software Reviews . . . . . . . . . . . . 78--80
Anonymous Problems . . . . . . . . . . . . . . . . 81--87
Gottfried E. Noether Media Highlights . . . . . . . . . . . . 88--95
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers and
Constance Reid An Interview With Mary Ellen Rudin . . . 114--137
Karl David Rencontres Reencountered . . . . . . . . 139--148
James D. Harper Estimating the Sum of Alternating Series 149--153
Richard J. Pulskamp Constructing a Map from a Table of
Intercity Distances . . . . . . . . . . 154--163
Joseph B. Kadane and
William A. Golomski and
Daniel A. Sankowsky and
Benjamin M. Perles Reader's Responses to the January '88
Forum: Should Mathematicians Teach
Statistics? . . . . . . . . . . . . . . 164--165
Chris W. Avery and
Frank P. Soler Applications of Transformations to
Numerical Integration . . . . . . . . . 166--173
George Manuel and
Amalia Santiago An Unexpected Appearance of the Golden
Ratio . . . . . . . . . . . . . . . . . 168--170
Stephen H. Friedberg An Alternate Proof of Cramer's Rule . . 171--171
Douglas S. Jungreis and
Erich Friedman How Many Bridge Auctions? . . . . . . . 171--172
Norman Schaumberger A General Form of the
Arithmetic--Geometric Mean Inequality
via the Mean Value Theorem . . . . . . . 172--173
Keith Matthews Algorithm of The Bi-Month . . . . . . . 174--176
Franklin Demana and
Bert K. Waits Pitfalls in Graphical Computation, or
Why a Single Graph Isn't Enough . . . . 177--183
L. Carl Leinbach and
Bill Parker Software Reviews . . . . . . . . . . . . 184--185
Anonymous Problems . . . . . . . . . . . . . . . . 186--193
Thomas F. Banchoff and
Thomas Banchoff Media Highlights . . . . . . . . . . . . 194--202
Anonymous Editorial Board . . . . . . . . . . . . ??
Peter Flusser Theory, Simulation and Reality . . . . . 210--222
F. Alexander Norman Parameter-generated Loci of Critical
Points of Polynomials . . . . . . . . . 223--229
Howard Lewis Penn Ties at Rotation . . . . . . . . . . . . 230--239
Richard L. Francis Mathematical Haystacks: Another Look at
Repunit Numbers . . . . . . . . . . . . 240--246
Joseph Wiener and
Will Watkins A Classroom Approach to Involutions . . 247--250
Joseph Wiener and
Henjin Chi and
Hushang Poorkarimi Involutions and Problems Involving
Perimeter and Area . . . . . . . . . . . 250--252
Leonard Gillman More on the Series for In 2 . . . . . . 252--253
Antal E. Fekete Apropos Predetermined Determinants . . . 254--257
James C. Kirby An Efficient Logarithm Algorithm for
Calculators . . . . . . . . . . . . . . 257--260
David P. Kraines and
David A. Smith A Computer in the Classroom: The Time is
Right . . . . . . . . . . . . . . . . . 261--267
R. S. Cunningham and
David A. Smith The Compleat Mathematics Software
Database . . . . . . . . . . . . . . . . 268--289
Anonymous Problems . . . . . . . . . . . . . . . . 290--294
Anonymous Media Highlights . . . . . . . . . . . . 295--300
Anonymous Editorial Board . . . . . . . . . . . . ??
Beverly L. Brechner and
John C. Mayer Antoine's Necklace or How to Keep a
Necklace From Falling Apart . . . . . . 306--320
Xun-Cheng Huang A Discrete L'Hôpital's Rule . . . . . . . 321--329
Robert I. Jewett and
Kenneth A. Ross Random Walks on Z . . . . . . . . . . . 330--342
Simon M. Goberstein Evaluating ``Uniformly Filled''
Determinants . . . . . . . . . . . . . . 343--345
Angela B. Shiflet Musical Notes . . . . . . . . . . . . . 345--347
Paolo Montuchi and
Warren Page Behold! Two Extremum Problems (and the
Arithmetic--Geometic Mean Inequality) 347--347
Richard E. Pfiefer Bounds on the Perimeter of an Ellipse
via Minkowski Sums . . . . . . . . . . . 348--350
Jim Howard and
Joe Howard Equivalent Inequalities . . . . . . . . 350--352
Mark Bridger Looking at the Mandelbrot Set . . . . . 353--363
Harley Flanders and
Alan F. Tomala Algorithm of The Bi-Month . . . . . . . 364--367
L. Carl Leinbach and
Thomas Hannula and
Daniel G. Lamet Software Reviews . . . . . . . . . . . . 367--369
Anonymous Problems . . . . . . . . . . . . . . . . 370--373
Anonymous Media Highlights . . . . . . . . . . . . 374--378
Anonymous Editorial Board . . . . . . . . . . . . ??
Warren Page A Farewell Editorial . . . . . . . . . . 386--386
David C. Hoaglin Using Leverage and Influence to
Introduce Regression Diagnostics . . . . 387--416
Chester J. Salwach Codes that Detect and Correct Errors . . 402--416
Duane W. DeTemple The Generalized Polygonal Cycloid . . . 417--419
Danny W. Turner and
Dean M. Young and
Virgil R. Marco Maybe the Price Doesn't Have to be
Right: Analysis of a Popular TV Game
Show . . . . . . . . . . . . . . . . . . 419--421
N. S. Mendelsohn Amalgamation of Formulae for Sequences 421--423
James E. White Teaching with CAL: a Mathematics
Teaching and Learning Environment . . . 424--443
Harley Flanders Algorithm of The Bi-Month . . . . . . . 444--447
Anonymous Problems . . . . . . . . . . . . . . . . 448--450
Anonymous Media Highlights . . . . . . . . . . . . 451--454
Anonymous Editorial Board . . . . . . . . . . . . ??
G. L. Alexanderson A Conversation with Saunders Mac Lane 2--26
Howard K. Justice Equality in Overlapping Gravitational
Fields . . . . . . . . . . . . . . . . . 27--31
James Caveny and
Warren Page The Fundamental Periods of Sums of
Periodic Functions . . . . . . . . . . . 32--41
Barnabas B. Hughes Hippocrates and Archytas Double the
Cube: a Heuristic Interpretation . . . . 42--48
Anonymous Fallacies, Flaws, and Flimflam . . . . . 49--50
Roger B. Nelsen The Double-Angle Formulas . . . . . . . 51--51
D. F. Bailey Differentials and Elementary Calculus 52--53
James C. Reber Pseudorandom Number Generators in a
Four-Bit Computer System . . . . . . . . 54--55
Barthel W. Huff Conditional Expectations and the
Correlation Function . . . . . . . . . . 55--57
Norman Schaumberger and
Bert Kabak Another Proof of Jensen's Inequality . . 57--58
Enzo R. Gentile Pythagorean Theorem: $ a \cdot a' + b
\cdot b' = c \cdot c' $ . . . . . . . . 58--58
Tommy Wright A Note on Pascal's Triangle and Simple
Random Sampling . . . . . . . . . . . . 59--66
Roland di Franco Software Review . . . . . . . . . . . . 67--67
Anonymous Problems . . . . . . . . . . . . . . . . 68--79
Anonymous Guidelines for Authors . . . . . . . . . 80--80
Anonymous Media Highlights . . . . . . . . . . . . 81--86
Anonymous Editorial Board . . . . . . . . . . . . ??
Cliff Long and
Thomas Hern Graphing the Complex Zeros of
Polynomials Using Modulus Surfaces . . . 98--105
May Beresin and
Eugene Levine and
John Winn A Chessboard Coloring Problem . . . . . 106--114
Alan H. Schoenfeld The Curious Fate of an Applied Problem 115--123
William T. Trotter On-Line Partitioning of Partially
Ordered Sets . . . . . . . . . . . . . . 124--131
Anonymous Fallacies, Flaws, and Flimflam . . . . . 132--133
Charles G. Moore To View an Ellipse in Perspective . . . 134--136
David A. Smith What's Significant about a Digit? . . . 136--139
Don Redmond Finding Rational Roots of Polynomials 139--141
Norman Schaumberger Another Proof of Chebysheff's Inequality 141--142
Donald R. Snow Spreadsheets, Power Series, Generating
Functions, and Integers . . . . . . . . 143--152
Frank S. T. Hsiao The Simplex Method of Linear Programming
on Microcomputer Spreadsheets . . . . . 153--160
Hal Schlais and
Walter Zimmermann Software Reviews . . . . . . . . . . . . 161--162
Anonymous Problems . . . . . . . . . . . . . . . . 163--173
Doris Schattschneider Media Highlights . . . . . . . . . . . . 174--181
Anonymous Editorial Board . . . . . . . . . . . . ??
Arthur C. Segal Subharmonic Series . . . . . . . . . . . 194--200
William C. Waterhouse Two Elementary Proofs of an Inequality
(and $ 1 1 / 2 $ Better Ones) . . . . . 201--205
Lowell W. Beineke Are Graphs Finally Surfacing? . . . . . 206--225
Anonymous Fallacies, Flaws, and Flimflam . . . . . 226--227
David P. Doane Using Median Splits to Motivate Learning 228--229
Roger C. Alperin The Matrix of a Rotation . . . . . . . . 230--230
Roger B. Nelsen The Root Mean Square-Arithmetic
Mean--Geometric Mean-Harmonic Mean
Inequality . . . . . . . . . . . . . . . 231--231
William E. Rosenthal Lattices of Trigonometric Identities . . 232--234
Arnold J. Insel A Direct Proof of the Integral Formula
for Arctangent . . . . . . . . . . . . . 235--237
John H. Mathews and
Harris S. Shultz Riemann Integral of $ \cos x $ . . . . . 237--237
Richard D. Neidinger Automatic Differentiation and APL . . . 238--251
Albyn Jones and
Amberse Banks and
Judith L. Clarke Software Reviews . . . . . . . . . . . . 252--255
Anonymous Problems . . . . . . . . . . . . . . . . 256--265
Peter W. Renz Media Highlights . . . . . . . . . . . . 266--273
Anonymous Editorial Board . . . . . . . . . . . . ??
Israel Kleiner Evolution of the Function Concept: a
Brief Survey . . . . . . . . . . . . . . 282--300
Daniel B. Widdis and
R. Bruce Richter It's Magic! Multiplication Theorems for
Magic Squares . . . . . . . . . . . . . 301--306
Harold Reiter and
David Ritchie A Complete Solution to the Magic
Hexagram Problem . . . . . . . . . . . . 307--316
Anonymous Fallacies, Flaws, and Flimflam . . . . . 317--319
Norman Schaumberger The AM--GM Inequality via $ x^{1 / x} $ 320--320
Lloyd Olson Where There Is Pattern, There is
Significance . . . . . . . . . . . . . . 321--321
Stephen H. Friedberg The Power Rule and the Binomial Formula 322--322
Herb Silverman A Simple Auxiliary Function for the Mean
Value Theorem . . . . . . . . . . . . . 323--323
Lawrence O. Cannon Locating Multiples of Primes in Pascal's
Triangle . . . . . . . . . . . . . . . . 324--328
Alan Gorfin Evaluating the Sum of the Series $
\sum_{k = 1}^\infty k^j / M^k $ . . . . 329--331
Michael Gemignani Copyright Law As It Applies to Computer
Software . . . . . . . . . . . . . . . . 332--338
Warren Page Software Reviews . . . . . . . . . . . . 339--342
Anonymous Problems . . . . . . . . . . . . . . . . 343--354
Barry Schiller and
Helen Salzberg and
Richard K. Guy Media Highlights . . . . . . . . . . . . 355--362
Anonymous Editorial Board . . . . . . . . . . . . ??
Mogens Esrom Larsen The Eternal Triangle --- a History of a
Counting Problem . . . . . . . . . . . . 370--384
J. N. Boyd and
P. N. Raychowdhury Discrete Dirichlet Problems, Convex
Coordinates, and a Random Walk on a
Triangle . . . . . . . . . . . . . . . . 385--392
J. J. Price Learning Mathematics Through Writing:
Some Guidelines . . . . . . . . . . . . 393--401
Anonymous Acknowledgement . . . . . . . . . . . . 402--402
Anonymous Fallacies, Flaws, and Flimflam . . . . . 403--404
Elgin H. Johnston An Alternative to Changing the Order of
Integration . . . . . . . . . . . . . . 405--408
Kenneth R. Kundert Sensitive Questions and Randomized
Response Techniques . . . . . . . . . . 409--411
G. Ervynck and
P. Igodt Power Series and Exponential Generating
Functions . . . . . . . . . . . . . . . 411--415
M. S. Klamkin and
V. N. Murty Generalizations of a Complex Number
Identity . . . . . . . . . . . . . . . . 415--416
Norman Schaumberger A Generalization of $ \lim_{n \to \infty
} \sqrt [n]{n!} / n = e^{-1} $ . . . . . 416--418
J. Hillel Notational Collisions . . . . . . . . . 418--422
John Selden and
Annie Selden Graphing with the HP-28S . . . . . . . . 423--432
David P. Kraines and
Vivian Y. Kraines and
David A. Smith and
David P. Kraines and
Vivian Y. Kraines and
David A. Smith and
David P. Kraines and
Vivian Y. Kraines and
David A. Smith Classroom Computer Capsules . . . . . . 433--438
Howard Lewis Penn Software Reviews . . . . . . . . . . . . 439--441
Anonymous Problems . . . . . . . . . . . . . . . . 442--451
Robert L. Devaney Media Highlights . . . . . . . . . . . . 452--459
Anonymous Editorial Board . . . . . . . . . . . . ??
George D. Gopen and
David A. Smith What's an Assignment Like You Doing in a
Course Like This?: Writing to Learn
Mathematics . . . . . . . . . . . . . . 2--19
Gilbert Strang Sums and Differences vs. Integrals and
Derivatives . . . . . . . . . . . . . . 20--27
Robert Hanson Minimum Dimension for a Square Matrix of
Order $n$ . . . . . . . . . . . . . . . 28--34
Anonymous Flaws, Fallacies, and Flimflam . . . . . 35--36
Peter Schumer Strings of Strongly Composite Integers
and Invisible Lattice Points . . . . . . 37--40
Keith A. Struss Exploring the Volume-Surface Area
Relationship . . . . . . . . . . . . . . 40--43
Mark E. Saul $ \Sin^2 x $: a Sheep in Wolf's Clothing 43--44
Bernard W. Banks A Rich Differential Equation for
Computer Demonstrations . . . . . . . . 45--50
Daniel S. Yates and
John H. Mathews and
David R. Hill Classroom Computer Capsules . . . . . . 51--56
David P. Kraines and
Vivian Y. Kraines Software Reviews . . . . . . . . . . . . 57--64
Anonymous Problems and Solutions . . . . . . . . . 65--72
Martin E. Flashman Media Highlights . . . . . . . . . . . . 73--80
Anonymous Editorial Board . . . . . . . . . . . . ??
William B. Gearhart and
Harris S. Shultz The Function $ \sin x / x $ . . . . . . 90--99
Dean S. Clark and
James T. Lewis Herbert and the Hungarian Mathematician:
Avoiding Certain Subsequence Sums . . . 100--104
Reuben Hersh Let's Teach Philosophy of Mathematics! 105--111
P. D. Weidman and
K. Pfendt On the Radial Packing of Circles in the
Plane . . . . . . . . . . . . . . . . . 112--120
Bert K. Waits and
Franklin Demana A Hidden Case of Negative Amortization 121--126
Anonymous Fallacies, Flaws, and Flimflam . . . . . 127--128
John W. Dawson, Jr. Hanging a Bird Feeder: Food for Thought 129--130
Marvin Marcus Determinants of Sums . . . . . . . . . . 130--135
Carsten Thomassen and
Herbert S. Wilf On `Uniformly Filled' Determinants . . . 135--137
Sidney H. Kung and
Yap S. Chua A Zero-Row Reduction Algorithm for
Obtaining the gcd of Polynomials . . . . 138--141
David P. Kraines and
Vivian Y. Kraines and
David A. Smith and
David P. Kraines and
Vivian Y. Kraines and
David A. Smith Classroom Computer Capsules . . . . . . 142--145
Alan Hoenig Software Reviews . . . . . . . . . . . . 146--149
Anonymous Problems and Solutions . . . . . . . . . 150--157
Martin E. Flashman Media Highlights . . . . . . . . . . . . 158--165
Anonymous Editorial Board . . . . . . . . . . . . ??
D. J. Albers and
G. L. Alexanderson A Conversation with Robin Wilson . . . . 178--195
Mark F. Schilling The Longest Run of Heads . . . . . . . . 196--207
Wilbur J. Hildebrand Connecting the Dots Parametrically: an
Alternative to Cubic Splines . . . . . . 208--215
Anonymous Fallacies, Flaws, and Flimflam . . . . . 216--218
Diane Johnson and
Roy Dowling Ways of Looking at n! . . . . . . . . . 219--220
John S. Robertson Proofs by --- Tion . . . . . . . . . . . 220--222
Stephan C. Carlson and
Jerry M. Metzger A Recursively Computed Limit . . . . . . 222--224
Douglass L. Grant Moments on a Rose Petal . . . . . . . . 225--227
Hervé Lehning Computer-Aided or Analytic Proof? . . . 228--239
David P. Kraines and
Vivian Y. Kraines and
David A. Smith Classroom Computer Capsules: Binary
Operations . . . . . . . . . . . . . . . 240--241
Roland di Franco and
T. J. Mahar and
Tyre A. Newton and
Tyre A. Newton and
Leonard G. Henscheid Software Reviews . . . . . . . . . . . . 242--245
Anonymous Problems and Solutions . . . . . . . . . 246--254
Martin E. Flashman Media Highlights . . . . . . . . . . . . 255--262
Anonymous Editorial Board . . . . . . . . . . . . ??
Herbert S. Wilf Self-esteem in Mathematicians . . . . . 274--277
David Singmaster Triangles with Integer Sides and Sharing
Barrels . . . . . . . . . . . . . . . . 278--285
Agnes Arvai Wieschenberg The Birth of the Eötvös Competition . . . 286--293
Miriam P. Cooney and
Jacqueline M. Dewar and
Patricia Clark Kenschaft and
Vivian Kraines and
Brenda Latka and
Barbara LiSanti Recruitment and Retention of Students in
Undergraduate Mathematics . . . . . . . 294--301
Anonymous Fallacies, Flaws, and Flimflam . . . . . 302--304
Roger H. Marty The Number of Paths in a Rooted Binary
Tree of Infinite Height . . . . . . . . 305--307
David Horowitz Tabular Integration by Parts . . . . . . 307--311
Russell Jay Hendel $ (x^n)' = n x^{n - 1} $: Six Proofs . . 312--313
Steven Schonefeld Some Examples Illustrating Richardson's
Improvement . . . . . . . . . . . . . . 314--322
Jim R. Ridenhour Spiders, Computers, and Markov Chains 323--326
David P. Kraines and
Vivian Y. Kraines and
David A. Smith Classroom Computer Capsule: The Cauchy
Integral Formula . . . . . . . . . . . . 327--329
Warren Page and
Raymond N. Greenwell and
Tyre A. Newton and
Leonard G. Henscheid Software Reviews . . . . . . . . . . . . 330--333
Anonymous Problems and Solutions . . . . . . . . . 334--341
Martin E. Flashman Media Highlights . . . . . . . . . . . . 342--349
Anonymous Editorial Board . . . . . . . . . . . . ??
E. John Hornsby, Jr. Geometrical and Graphical Solutions of
Quadratic Equations . . . . . . . . . . 362--378
M. R. Cullen Moiré Fringes and the Conic Sections . . 370--378
S. C. Althoen and
M. F. Wyneken A Mathematical Field Day . . . . . . . . 379--383
Daniel Cass and
Gerald Wildenberg Relations between Surface Area and
Volume in Lakes . . . . . . . . . . . . 384--389
Bart Braden China's 1989 National College Entrance
Examination . . . . . . . . . . . . . . 390--393
Anonymous Fallacies, Flaws, and Flimflam . . . . . 394--396
Loretta McCarty Polar Summation . . . . . . . . . . . . 397--398
Winston Phrobis The Age of the Solar System . . . . . . 399--400
Raymond A. McGivney, Jr. Forward Homework --- a Motivational Tool 400--402
Herb Silverman Trigonometric Identities through
Calculus . . . . . . . . . . . . . . . . 403--403
J. J. Price Algorithms for Evaluation of Polynomials 404--405
Doug Hardin and
Gilbert Strang A Thousand Points of Light . . . . . . . 406--409
Robert Lopez and
John Mathews Using a Computer Algebra System to Solve
for Maxima and Minima . . . . . . . . . 410--414
David P. Kraines and
Vivian Y. Kraines and
David A. Smith and
David P. Kraines and
Vivian Y. Kraines and
David A. Smith and
David P. Kraines and
Vivian Y. Kraines and
David A. Smith Classroom Computer Capsules . . . . . . 415--419
L. Carl Leinbach Software Reviews . . . . . . . . . . . . 420--422
Anonymous Problems and Solutions . . . . . . . . . 423--430
Martin E. Flashman Media Highlights . . . . . . . . . . . . 431--437
Anonymous Editorial Board . . . . . . . . . . . . ??
Robert L. Devaney Special Issue on Dynamical Systems . . . 2--2
Gilbert Strang A Chaotic Search for $i$ . . . . . . . . 3--12
James T. Sandefur Discrete Dynamical Modeling . . . . . . 13--22
Robert L. Devaney The Orbit Diagram and the Mandelbrot Set 23--38
Anonymous Fallacies, Flaws, and Flimflam . . . . . 39--41
Larry Blaie Theory vs. Computation in Some Very
Simple Dynamical Systems . . . . . . . . 42--44
Paul C. Matthews and
Steven H. Strogatz Chaotic Mappings and Probability
Distributions . . . . . . . . . . . . . 45--47
Richard Parris The Root-Finding Route to Chaos . . . . 48--55
Stephen J. Willson Teaching about Fractals . . . . . . . . 56--59
Yves Nievergelt Classroom Computer Capsule: Fractals
Illustrate the Mathematical Way of
Thinking . . . . . . . . . . . . . . . . 60--64
Jonathan Choate Software Reviews . . . . . . . . . . . . 65--69
Anonymous Problems and Solutions . . . . . . . . . 70--76
Thomas Scavo Media Highlights . . . . . . . . . . . . 77--84
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers Interview With Irving Kaplansky . . . . 98--117
Howard Eves Two Surprising Theorems on Cavalieri
Congruence . . . . . . . . . . . . . . . 118--124
Thomas L. Moore Using Euler's Formula to Solve Plane
Separation Problems . . . . . . . . . . 125--130
Anonymous Fallacies, Flaws, and Flimflam . . . . . 131--133
Keith M. Kendig Single Equations Can Draw Pictures . . . 134--139
Xiao-peng Xu The Snowplow Problem Revisited . . . . . 139--139
David A. Rose The Differentiability of $ \Sin x $ . . 139--142
Enzo R. Gentile Another Proof of the Irrationality of $
\sqrt {2} $ . . . . . . . . . . . . . . 143--143
Anonymous Secrets of the Faro . . . . . . . . . . 144--147
William Fisher and
Richard Campbell Investigating Spirolaterals Through LOGO 148--159
David P. Kraines and
Vivian Y. Kraines and
David A. Smith Classroom Computer Capsule:
Predator-Prey Model . . . . . . . . . . 160--162
Douglas Campbell Software Reviews . . . . . . . . . . . . 163--166
Anonymous Problems and Solutions . . . . . . . . . 167--172
Ed Barbeau Media Highlights . . . . . . . . . . . . 173--180
Anonymous Editorial Board . . . . . . . . . . . . ??
Joseph A. Gallian The Mathematics of Identification
Numbers . . . . . . . . . . . . . . . . 194--202
Doris Schattschneider Counting It Twice . . . . . . . . . . . 203--211
Abraham Arcavi and
Maxim Bruckheimer Reading Bombelli's $x$-purgated Algebra 212--219
Anonymous Fallacies, Flaws, and Flimflam . . . . . 220--223
Joel K. Haack Clapping Music --- a Combinatorial
Problem . . . . . . . . . . . . . . . . 224--227
Herbert R. Bailey `Hidden' Boundaries in Constrained
Max-Min Problems . . . . . . . . . . . . 227--229
Norman Schaumberger Another Proof of a Familiar Inequality 229--230
Henry Mark Smith Positivity from Evaluation of a Single
Point . . . . . . . . . . . . . . . . . 230--231
L. R. King and
Harold B. Reiter Graceful Graphs and Sparsely Marked
Rulers . . . . . . . . . . . . . . . . . 232--234
Richard F. Maruszewski, Jr. Programs for a Logic Course . . . . . . 235--241
Helen Skala Contour Maps --- a Visual Experience . . 241--244
David P. Kraines Classroom Computer Capsules: Rotations
in Space and Orthogonal Matrices . . . . 245--247
Joan Wyzkoski Weiss Software Reviews . . . . . . . . . . . . 248--254
Anonymous Problems and Solutions . . . . . . . . . 255--260
Annie Selden Media Highlights . . . . . . . . . . . . 261--268
Anonymous Editorial Board . . . . . . . . . . . . ??
William Dunham Euler and the Fundamental Theorem of
Algebra . . . . . . . . . . . . . . . . 282--293
Lee Zia Using the Finite Difference Calculus to
Sum Powers of Integers . . . . . . . . . 294--300
K. R. S. Sastry Triangles in a Lattice Parabola . . . . 301--306
Anonymous Fallacies, Flaws, and Flimflam . . . . . 307--310
Elliot Winston A Carpenter's Ellipse . . . . . . . . . 311--312
Richard E. Pfiefer Stacking Ellipses . . . . . . . . . . . 312--313
G. D. Chakerian The Isoperimetric Quotient: Another Look
at an Old Favorite . . . . . . . . . . . 313--315
Lee H. Minor A Productive Error in a Trigonometry
Text . . . . . . . . . . . . . . . . . . 315--318
Anthony Lo Bello The Volume and Centroid of the Step
Pyramid of Zoser . . . . . . . . . . . . 318--321
John H. Mathews The Sum is One . . . . . . . . . . . . . 322--322
Dennis Kletzing Coset Products in Rings . . . . . . . . 323--326
Paul B. Massell Using Computer Graphics to Help Analyze
Complicated Functions . . . . . . . . . 327--331
Stan Byrd and
Terry Walters Classroom Computer Capsule: Graphs of
Rational Functions for Computer Assisted
Calculus . . . . . . . . . . . . . . . . 332--334
J. A. Hummel and
W. P. Nanry Software Review . . . . . . . . . . . . 335--342
Anonymous Problems and Solutions . . . . . . . . . 343--348
J. J. Tattersall Media Highlights . . . . . . . . . . . . 349--356
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers and
G. L. Alexanderson A Conversation with Ivan Niven . . . . . 370--402
Anonymous Fallacies, Flaws, and Flimflam . . . . . 403--406
Leonard Gillman More on Tabular Integration by Parts . . 407--410
Leroy F. Meyers Four Crotchets on Elementary Integration 410--413
Xun-Cheng Huang A Shortcut in Partial Fractions . . . . 413--415
Russell Jay Hendel Differentiation via Partial Fractions: a
Case against CAS . . . . . . . . . . . . 415--417
Daniel A. Moran Graphs and Derivatives of the Inverse
Trig Functions . . . . . . . . . . . . . 417--417
Anonymous Reward of the Rings . . . . . . . . . . 418--420
T. N. Subramaniam and
D. E. G. Malm Reduction Formulas Revisited . . . . . . 421--429
Mark Bridger Image Expansion in Integer Arithmetic 429--435
Peter Turner and
Craig Bailey Software Review . . . . . . . . . . . . 436--442
Anonymous Problems and Solutions . . . . . . . . . 443--449
Kathirgama Nathan and
Kathirgama Nathan Media Highlights . . . . . . . . . . . . 450--457
Kathirgama Nathan Review: \booktitleFractals for the
Classroom. Part One: Introduction to
Fractals and Chaos by H. O. Peitgen, H.
Jürgens, D. Saupe; \booktitleFractals for
the Classroom. Part Two: Complex Systems
and Mandelbrot Set by H. O. Peitgen, H.
Jürgens, D. Saupe . . . . . . . . . . . . 455--456
Anonymous Editorial Board . . . . . . . . . . . . ??
George Markowsky Misconceptions about the Golden Ratio 2--19
Leon M. Hall Trochoids, Roses, and Thorns-Beyond the
Spirograph . . . . . . . . . . . . . . . 20--35
Anonymous Fallacies, Flaws, and Flimflam . . . . . 36--38
Gregory Fredricks and
Roger B. Nelsen Summation by Parts . . . . . . . . . . . 39--42
Carlos C. Huerta Who Needs the Sine Anyway? . . . . . . . 43--44
Marvin Marcus Determinantal Loci . . . . . . . . . . . 44--47
Aaron D. Abrams and
Matteo J. Paris The Probability That (a, b ) = 1 . . . . 47--47
Lee H. Minor Visualization of Limits and Limits of
Visualization . . . . . . . . . . . . . 48--51
George Mackiw Number Theory and Linear Algebra: Exact
Solutions of Integer Systems . . . . . . 52--58
Robert J. Hill and
Robert D. Bechtel Classroom Computer Capsules:
Eigenvectors and Jordan Bases Using
Symbolic Programs . . . . . . . . . . . 59--63
Lillie R. F. Crowley and
J. Stephen Ott Software Review . . . . . . . . . . . . 64--68
Anonymous Problems and Solutions . . . . . . . . . 69--76
Victor J. Katz Media Highlights . . . . . . . . . . . . 77--84
Anonymous Editorial Board . . . . . . . . . . . . ??
G. L. Alexanderson A Conversation with Leon Bankoff . . . . 98--117
Dana N. Mackenzie Triquetras and Porisms . . . . . . . . . 118--131
Mark Bridger Calculus and Computer Vision . . . . . . 132--141
Anonymous Fallacies, Flaws, And Flimflam . . . . . 142--144
Paul Chacon Relative Maxima or Minima for a Function
of Two Variables: a Neglected Approach 145--146
Tom Farmer and
Fred Gass Physical Demonstrations in the Calculus
Classroom . . . . . . . . . . . . . . . 146--148
James C. Kirby Rubberbanding and Holding Out . . . . . 148--149
David W. Jensen and
Eric R. Bussian A Number-Theoretic Approach to Counting
Subgroups of Dihedral Groups . . . . . . 150--152
Raymond J. Collins Approximating Series . . . . . . . . . . 153--157
Jeanette R. Palmiter Software Reviews . . . . . . . . . . . . 158--161
Anonymous Problems and Solutions . . . . . . . . . 162--167
Peter Ross Media Highlights . . . . . . . . . . . . 168--175
Anonymous Editorial Board . . . . . . . . . . . . ??
Nitsa Movshovitz-Hadar and
Alla Shmukler Infinitely Many Different Quartic
Polynomial Curves . . . . . . . . . . . 186--195
H. Guggenheimer Systems of Linear Differential Equations
by Laplace Transform . . . . . . . . . . 196--202
Anonymous Fallacies, Flaws, and Flimflam . . . . . 203--206
Roger B. Nelsen The Relationship between Hyperbolic and
Exponential Functions --- Revisited . . 207--208
John H. Mathews A Geometric Proof of $ \lim_{d \to 0^+}(
- d \ln d) = 0 $ . . . . . . . . . . . . 209--209
Vincent P. Schielack, Jr. Summing Geometric Series by Holding a
Tournament . . . . . . . . . . . . . . . 210--211
François Dubeau Weighted Means of Order $r$ and Related
Inequalities: an Elementary Approach . . 211--213
Stephen L. Davis Square-Free Sets on Square Grids . . . . 214--224
Anne M. Burns The Flowering of String Rewriting
Systems . . . . . . . . . . . . . . . . 225--236
J. M. A. Danby Classroom Computer Capsules: Fireworks 237--240
Anonymous Software Reviews . . . . . . . . . . . . 241--246
Anonymous Problems and Solutions . . . . . . . . . 247--252
James J. Kaput Media Highlights . . . . . . . . . . . . 253--260
Anonymous Editorial Board . . . . . . . . . . . . ??
Peter Hilton The Joy of Mathematics: a Mary P.
Dolciani Lecture . . . . . . . . . . . . 274--281
Bennett Eisenberg and
Samir Khabbaz Optimal Locations . . . . . . . . . . . 282--289
LeRoy A. Franklin Using Simulation to Study Linear
Regression . . . . . . . . . . . . . . . 290--295
David M. Bressoud How Should We Introduce Integration? . . 296--298
David Carlson and
Charles R. Johnson and
David Lay and
A. Duane Porter Gems of Exposition in Elementary Linear
Algebra . . . . . . . . . . . . . . . . 299--303
Anonymous Fallacies, Flaws, and Flimflam . . . . . 304--307
J. Thoo Timing is Everything . . . . . . . . . . 308--309
V. Ngo and
S. Ouzomgi Teaching the Laplace Transform Using
Diagrams . . . . . . . . . . . . . . . . 309--312
Susan Forman A Serendipitous Application of the
Pythagorean Triplets . . . . . . . . . . 312--314
Anonymous Erratum: Relative Maxima or Minima for a
Function of Two Variables . . . . . . . 314--314
George T. Gilbert and
Loren C. Larson A Sliding Block Problem . . . . . . . . 315--319
Lyndell M. Kerley and
William P. Dotson Using Fourier Analysis in Digital Signal
Processing . . . . . . . . . . . . . . . 320--328
David R. Hill Classroom Computer Capsules:
Interpolating Polynomials and Their
Coordinates Relative to a Basis . . . . 329--333
Bruce E. Sagan Software Reviews . . . . . . . . . . . . 334--339
Anonymous Problems and Solutions . . . . . . . . . 340--347
Frank Swetz Media Highlights . . . . . . . . . . . . 348--355
Anonymous Editorial Board . . . . . . . . . . . . ??
Uri Treisman Studying Students Studying Calculus: a
Look at the Lives of Minority
Mathematics Students in College . . . . 362--372
Lester H. Lange and
James W. Miller A Random Ladder Game: Permutations,
Eigenvalues, and Convergence of Markov
Chains . . . . . . . . . . . . . . . . . 373--385
Shmuel Avital and
Edward Barbeau Commutativity of Polynomials . . . . . . 386--395
Daniel Drucker A Mathematical Roller Derby . . . . . . 396--401
Dean Clark Fallacies, Flaws, And Flimflam . . . . . 402--406
Elmer K. Hayashi Fibonacci Numbers, Recursion,
Complexity, and Induction Proofs . . . . 407--410
Abdus Sattar Gazdar Distance from a Point to a Plane with a
Variation on the Pythagorean Theorem . . 410--412
Ernest J. Eckert Primitive Pythagorean Triples . . . . . 413--417
Steven Schonefeld Rotation of Axes-Not Just for Conics . . 418--425
Sheldon P. Gordon Classroom Computer Capsules:
Individualized Computer Investigations
for Calculus . . . . . . . . . . . . . . 426--428
L. Carl Leinbach and
Edward A. Huff Software Reviews . . . . . . . . . . . . 429--434
Anonymous Problems and Solutions . . . . . . . . . 435--440
Richard Askey Media Highlights . . . . . . . . . . . . 441--448
Anonymous Editorial Board . . . . . . . . . . . . ??
Alan Tucker The Growing Importance of Linear Algebra
in Undergraduate Mathematics . . . . . . 3--9
Richard A. Brualdi and
Jennifer J. Q. Massey Some Applications of Elementary Linear
Algebra in Combinatorics . . . . . . . . 10--19
Gilbert Strang Graphs, Matrices, and Subspaces . . . . 20--28
David Carlson Teaching Linear Algebra: Must the Fog
Always Roll in? . . . . . . . . . . . . 29--40
David Carlson and
Charles R. Johnson and
David C. Lay and
A. Duane Porter The Linear Algebra Curriculum Study
Group Recommendations for the First
Course in Linear Algebra . . . . . . . . 41--46
Gerald J. Porter Linear Algebra and Affine Planar
Transformations . . . . . . . . . . . . 47--51
Dean Clark and
Dilip K. Datta Arithmetic Matrices and the Amazing
Nine-Card Monte . . . . . . . . . . . . 52--56
David C. Lay Subspaces and Echelon Forms . . . . . . 57--62
Richard L. Francis and
Constance J. Gardner Fallacies, Flaws, and Flimflam . . . . . 63--66
Thomas Hern Gaussian Elimination in Integer
Arithmetic: an Application of the \em
L-U Factorization . . . . . . . . . . . 67--71
Arnold J. Insel Rotation Matrices in the Plane without
Trigonometry . . . . . . . . . . . . . . 71--73
Melvin J. Maron and
Ghansham M. Manwani A Geometric Interpretation of the
Columns of the (Pseudo)Inverse of $A$ 73--75
Anonymous The Linear Transformation Associated
with a Graph . . . . . . . . . . . . . . 76--78
Donald R. LaTorre Iterative Methods in Introductory Linear
Algebra . . . . . . . . . . . . . . . . 79--88
Deane Arganbright Software Reviews . . . . . . . . . . . . 89--94
Anonymous Problems and Solutions . . . . . . . . . 95--100
David E. Flesner Media Highlights . . . . . . . . . . . . 101--108
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers and
Gerald L. Alexanderson A Conversation with Richard K. Guy . . . 122--148
Anonymous Fallacies, Flaws, and Flimflam . . . . . 149--154
P. Glaister Does What Goes Up Take the Same Time to
Come Down? . . . . . . . . . . . . . . . 155--158
Sherrie J. Nicol Integrals of Products of Sine and Cosine
with Different Arguments . . . . . . . . 158--160
Fred Richman A Circular Argument . . . . . . . . . . 160--162
John H. Wilson Permutation Puzzles . . . . . . . . . . 163--165
Lyndell Kerley and
Jeff Knisley Complex Vectors and Image Identification 166--174
Caspar R. Curjel and
John Sylvester A Computer Lab for Multivariable
Calculus . . . . . . . . . . . . . . . . 175--177
Frances Gulick Software Reviews . . . . . . . . . . . . 178--182
Anonymous Problems and Solutions . . . . . . . . . 183--190
Mark Kidwell Media Highlights . . . . . . . . . . . . 191--198
Anonymous Editorial Board . . . . . . . . . . . . ??
C. W. Groetsch Inverse Problems and Torricelli's Law 210--217
Barbara E. Reynolds The Algorists vs. the Abacists: an
Ancient Controversy on the Use of
Calculators . . . . . . . . . . . . . . 218--223
Donald Francis Young Local Conditions for Convexity and
Upward Concavity . . . . . . . . . . . . 224--228
Anonymous Fallacies, Flaws, and Flimflam . . . . . 229--232
P. L. Roe The Best Shape for a Tin Can . . . . . . 233--236
James E. Duemmel The Curious 1/3 . . . . . . . . . . . . 236--237
Lester H. Lange What is the Biggest Rectangle You Can
Put Inside a Given Triangle? . . . . . . 237--240
Margaret Cibes Old Calculus Chestnuts: Roast, or Light
a Fire? . . . . . . . . . . . . . . . . 241--243
Donald Teets Least Squares and Quadric Surfaces . . . 243--244
L. R. King and
Benjamin G. Klein The Doors . . . . . . . . . . . . . . . 245--246
Fabio Cavallini Fitting a Logistic Curve to Data . . . . 247--253
David Neal Determining Sample Sizes for Monte Carlo
Integration . . . . . . . . . . . . . . 254--259
Jerry Johnson Tangent Vectors and Orthogonal
Projections . . . . . . . . . . . . . . 259--262
L. Carl Leinbach Software Reviews . . . . . . . . . . . . 263--270
Anonymous Problems and Solutions . . . . . . . . . 271--276
Les Lange Media Highlights . . . . . . . . . . . . 277--284
Anonymous Editorial Board . . . . . . . . . . . . ??
Peter Hilton and
Jean Pedersen Geometry: a Gateway to Understanding . . 298--317
Roger Herz-Fischler A ``Very Pleasant Theorem'' . . . . . . 318--324
Sheldon P. Gordon Taylor Polynomial Approximations in
Polar Coordinates . . . . . . . . . . . 325--330
David Bange and
Linda Host Does a Parabola Have an Asymptote? . . . 331--342
Anonymous Fallacies, Flaws, and Flimflam . . . . . 343--346
Russell Euler Maclaurin Expansion of $ \Arctan x $ via
L'Hôspital's Rule . . . . . . . . . . . . 347--350
G. E. Bilodeau An Exponential Rule . . . . . . . . . . 350--351
Robert B. Gardner A Useful Notation for Rules of
Differentiation . . . . . . . . . . . . 351--352
H. L. Abbott Remarks Concerning ``Square-Free Sets on
Square Grids'' . . . . . . . . . . . . . 353--356
Antonio M. Lopez, Jr. Using PROLOG in Discrete Mathematics . . 357--365
Richard L. Hall Computer-Aided Delusions . . . . . . . . 366--369
Dennis DeTurck Software Reviews . . . . . . . . . . . . 370--376
Anonymous Problems and Solutions . . . . . . . . . 377--385
Anonymous Media Highlights . . . . . . . . . . . . 386--393
Anonymous Editorial Board . . . . . . . . . . . . ??
Dan Kalman Six Ways to Sum a Series . . . . . . . . 402--421
Jack Eidswick Two Trisectrices for the Price of One
Rolling Coin . . . . . . . . . . . . . . 422--430
Annie Selden and
John Selden Collegiate Mathematics Education
Research: What Would That Be Like? . . . 431--445
Stuart E. Mills Fallacies, Flaws, and Flimflam . . . . . 446--450
Roger W. Johnson How Does the NFL Rate the Passing
Ability of Quarterbacks? . . . . . . . . 451--453
Calvin Jongsma Stacking Ellipses-Revisited . . . . . . 453--453
Neil C. Schwertman and
Larry R. Dion Quadratic Confidence Intervals . . . . . 453--457
Carl Swenson and
André Yandl An Alternative Definition of the Number
$e$ . . . . . . . . . . . . . . . . . . 458--461
Maurino P. Bautista Software Reviews . . . . . . . . . . . . 462--471
Anonymous Problems and Solutions . . . . . . . . . 472--480
Anonymous Media Highlights . . . . . . . . . . . . 481--488
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers Freeman Dyson: Mathematician, Physicist,
and Writer . . . . . . . . . . . . . . . 2--21
Robert J. MacG. Dawson Towers of Powers Modulo $m$ . . . . . . 22--28
Reinhard C. Laubenbacher and
David J. Pengelley Eisenstein's Misunderstood Geometric
Proof of the Quadratic Reciprocity
Theorem . . . . . . . . . . . . . . . . 29--34
Anonymous Fallacies, Flaws, and Flimflam . . . . . 35--37
Norman Schaumberger Another Proof of the Formula $ e =
\sum_0^\infty (1 / n!) $ . . . . . . . . 38--39
Sheldon P. Gordon Riemann Sums and the Exponential
Function . . . . . . . . . . . . . . . . 39--40
Barry J. Arnow On Laplace's Extension of the Buffon
Needle Problem . . . . . . . . . . . . . 40--43
Frederick Gass Tangents to Conics, Eccentrically . . . 43--45
David M. Berman Lottery Drawings Often Have Consecutive
Numbers . . . . . . . . . . . . . . . . 45--47
Michael L. Treuden Frequencies of Digits in Factorials: an
Experimental Approach . . . . . . . . . 48--55
Eric R. Muller and
K. J. Srivastava Software Reviews . . . . . . . . . . . . 56--63
Anonymous Problems and Solutions . . . . . . . . . 64--70
Anonymous Media Highlights . . . . . . . . . . . . 71--76
Anonymous Editorial Board . . . . . . . . . . . . ??
Andrew Lenard and
Michael K. Brozinsky Kepler Orbits More Geometrico . . . . . 90--98
David Neal The Series $ \sum_{n = 1}^\infty n^m x^n
$ and a Pascal-like Triangle . . . . . . 99--101
Anthony P. Ferzola and
Sydney H. Kung Euler and Differentials . . . . . . . . 102--111
Reinhard C. Laubenbacher and
Michael Siddoway Great Problems of Mathematics: a Summer
Workshop for High School Students . . . 112--114
Robert Y. Suen Roots of Cubics via Determinants . . . . 115--117
Steve Benson Euclid's (Gaussian) Algorithm: a Lattice
Approach . . . . . . . . . . . . . . . . 118--124
Massimo Furi and
Mario Martelli Strictly Increasing Differentiable
Functions . . . . . . . . . . . . . . . 125--127
Anonymous Fallacies, Flaws, and Flimflam . . . . . 128--131
Yves Nievergelt Calculus Measures Tank Capacity and
Avoids Oil Spills . . . . . . . . . . . 132--136
Eric Key Disks, Shells, and Integrals of Inverse
Functions . . . . . . . . . . . . . . . 136--138
Russell Jay Hendel Approaches to the Formula for the $n$ th
Fibonacci Number . . . . . . . . . . . . 139--142
John H. Mathews The Integral of $ x^{1 / 2} $, etc. . . 142--144
Bill Juraschek Investigating Circles in the Poincaré
Disk Using \em Geometer's Sketchpad . . 145--154
James N. Boyd and
P. N. Raychowdhury Software Reviews . . . . . . . . . . . . 155--156
Anonymous Problems and Solutions . . . . . . . . . 157--163
Mark E. Saul Media Highlights . . . . . . . . . . . . 164--171
Anonymous Editorial Board . . . . . . . . . . . . ??
Bart Braden A Note from the Editor . . . . . . . . . 178--178
Robert Weinstock and
Roger B. Nelsen Isaac Newton: Credit Where Credit Won't
Do . . . . . . . . . . . . . . . . . . . 179--192
Curtis Wilson Newton's Orbit Problem: a Historian's
Response . . . . . . . . . . . . . . . . 193--200
Richard S. Westfall and
Sidney H. Kung In Defense of Newton: His Biographer
Replies . . . . . . . . . . . . . . . . 201--205
A. P. French and
R. S. Hu In Defense of Newton: a Physicist's View 206--211
M. Nauenberg Newton's \booktitlePrincipia and
Inverse-Square Orbits . . . . . . . . . 212--222
Anonymous Fallacies, Flaws, and Flimflam . . . . . 223--225
Susan Jane Colley Calculus in the Brewery . . . . . . . . 226--227
R. H. Eddy and
R. Fritsch An Optimization Oddity . . . . . . . . . 227--229
Jeffrey Li-chieh Ho A Simple Geometric Proof of the Addition
Formula for the Sine . . . . . . . . . . 229--230
Ronald L. Persky Extending Bernoulli's Inequality . . . . 230--230
Anonymous Computer Corner . . . . . . . . . . . . 231--231
Patrick Costello Computing Jordan Canonical Forms . . . . 231--234
Anita E. Solow Software Reviews . . . . . . . . . . . . 235--239
Roger B. Nelsen Problems and Solutions . . . . . . . . . 240--246
Underwood Dudley Media Highlights . . . . . . . . . . . . 247--254
Anonymous Editorial Board . . . . . . . . . . . . ??
S. C. Althoen and
K. E. Schilling and
M. F. Wyneken Cutting Corners: a Four-gon Conclusion 266--279
Paulo Ribenboim Prime Number Records . . . . . . . . . . 280--290
Hardy Grant Leibniz and the Spell of the Continuous 291--294
Elena Anne Marchisotto and
Gholam-Ali Zakeri An Invitation to Integration in Finite
Terms . . . . . . . . . . . . . . . . . 295--308
Frank Burk Fallacies, Flaws, and Flimflam . . . . . 309--311
Duane W. DeTemple An Archimedean Property of the
Bicylinder . . . . . . . . . . . . . . . 312--314
Edward Rozema Round-off, Batting Averages, and
Ill-Conditioning . . . . . . . . . . . . 314--317
Mark Schwartz On the Distance from a Point to a Curve 317--319
Kirby C. Smith and
Vincent P. Schielack Parametric Equations and Planar Curves 319--321
Dmitri Thoro and
Linda Valdés Investigation of a Recurrence Relation 322--324
Anonymous Computer Corner . . . . . . . . . . . . 325--325
Stan Wagon A Mathematical Magic Trick . . . . . . . 325--326
Richard J. Pulskamp and
William J. Larkin III Using the Sign Function to Analyze
Graphs . . . . . . . . . . . . . . . . . 327--328
James P. Fink Software Reviews . . . . . . . . . . . . 329--333
Roger W. Johnson Problems and Solutions . . . . . . . . . 334--340
Jim Tattersall Media Highlights . . . . . . . . . . . . 341--348
Anonymous Editorial Board . . . . . . . . . . . . ??
Beverly West A Note from the Guest Editor . . . . . . 362--363
William E. Boyce New Directions in Elementary
Differential Equations . . . . . . . . . 364--371
John H. Hubbard What It Means to Understand a
Differential Equation . . . . . . . . . 372--384
Paul Blanchard Teaching Differential Equations with a
Dynamical Systems Viewpoint . . . . . . 385--393
Paul Davis Asking Good Questions about Differential
Equations . . . . . . . . . . . . . . . 394--400
Robert L. Borrelli and
Courtney S. Coleman Computers, Lies, and the Fishing Season 401--412
Martin Ehrismann Quenching a Thirst with Differential
Equations . . . . . . . . . . . . . . . 413--418
John H. Hubbard and
Jean Marie McDill and
Anne Noonburg and
Beverly H. West A New Look at the Airy Equation with
Fences and Funnels . . . . . . . . . . . 419--431
Anonymous Fallacies, Flaws, and Flimflam . . . . . 432--435
Roland Minton A Progression of Projectiles: Examples
from Sports . . . . . . . . . . . . . . 436--442
Thomas Gruszka A Balloon Experiment in the Classroom 442--444
Herman Gollwitzer Matrix Patterns and Undetermined
Coefficients . . . . . . . . . . . . . . 444--448
J. M. McDill and
Bjòrn Felsager The Lighter Side of Differential
Equations . . . . . . . . . . . . . . . 448--452
David O. Lomen Experiments with Probes in the
Differential Equations Classroom . . . . 453--457
Andrew Flint and
Ron Wood Software Reviews . . . . . . . . . . . . 458--461
Anonymous Problems and Solutions . . . . . . . . . 462--467
Anonymous Media Highlights . . . . . . . . . . . . 468--473
Anonymous Editorial Board . . . . . . . . . . . . ??
Heinrich W. Guggenheimer and
Alan S. Edelman and
Charles R. Johnson A Simple Estimate of the Condition
Number of a Linear System . . . . . . . 2--5
J. G. Simmonds A New Look at an Old Function, $ e^{i
\theta } $ . . . . . . . . . . . . . . . 6--10
Paul Fjelstad The Repeating Integer Paradox . . . . . 11--15
Farhad Riahi An Early Iterative Method for the
Determination of $ \sin 1^\circ $ . . . 16--21
James A. Walsh The Dynamics of Newton's Method for
Cubic Polynomials . . . . . . . . . . . 22--28
R. Bruce Crofoot Continuity on a Set . . . . . . . . . . 29--30
Duane Kouba Can We Use the First Derivative to
Determine Inflection Points? . . . . . . 31--34
Anonymous Fallacies, Flaws, and Flimflam . . . . . 35--38
Roger Nelsen Symmetry and Integration . . . . . . . . 39--41
J. S. Hartzler Designing a Rose Cutter . . . . . . . . 41--43
Robert Paré A Visual Proof of Eddy and Fritsch's
Minimal Area Property . . . . . . . . . 43--44
William E. Boyce and
Joseph G. Ecker The Computer-oriented Calculus Course at
Rensselaer Polytechnic Institute . . . . 45--50
Anne M. Burns Making Mountains from a Sum of Molehills 51--57
Lawrence G. Gilligan Software Reviews . . . . . . . . . . . . 58--65
Anonymous Problems and Solutions . . . . . . . . . 66--72
Marjorie Senechal Media Highlights . . . . . . . . . . . . 73--81
Anonymous Announcing $ 25$-Year \booktitleCMJ
Topic Index . . . . . . . . . . . . . . 82--82
Anonymous Acknowledgment . . . . . . . . . . . . . 83--83
Anonymous Editorial Board . . . . . . . . . . . . ??
John Ewing Can We See the Mandelbrot Set? . . . . . 90--99
Nigel Boston A Taylor-made Plug for Wiles' Proof . . 100--105
Dwight D. Freund A Genuine Application of Synthetic
Division, Descartes' Rule of Signs, and
All That Stuff . . . . . . . . . . . . . 106--110
T. G. Proctor Distinguished Oscillations of a Forced
Harmonic Oscillator . . . . . . . . . . 111--117
H. K. Krishnapriyan Eulerian Polynomials and Faulhaber's
Result on Sums of Powers of Integers . . 118--123
David Dennis and
Jere Confrey Functions of a Curve: Leibniz's Original
Notion of Functions and Its Meaning for
the Parabola . . . . . . . . . . . . . . 124--131
Anonymous Fallacies, Flaws, and Flimflam . . . . . 132--134
Anthony J. Macula The Point-Slope Formula Leads to the
Fundamental Theorem of Calculus . . . . 135--139
Pat Touhey Chebyshev's Theorem: a Geometric
Approach . . . . . . . . . . . . . . . . 139--141
Griffin Weber and
Glenn Weber Pizza Combinatorics . . . . . . . . . . 141--143
Robert C. Moore Visualizing the Group Homomorphism
Theorem . . . . . . . . . . . . . . . . 143--143
Tim Hesterberg The Spider's Spacewalk Derivation of $
\sin ' $ and $ \cos ' $ . . . . . . . . 144--145
Robert J. Hill and
Mark S. Mazur The Matrix Exponential Function and
Systems of Differential Equations Using
Derive . . . . . . . . . . . . . . . . . 146--151
L. Carl Leinbach Software Reviews . . . . . . . . . . . . 152--156
Anonymous Problems and Solutions . . . . . . . . . 157--162
Keith Devlin Media Highlights . . . . . . . . . . . . 163--170
Anonymous Editorial Board . . . . . . . . . . . . ??
Lawrence J. Wallen Kepler, the Taxicab Metric, and Beyond:
an Isoperimetric Primer . . . . . . . . 178--190
Steven Schwartzman Number Words in English . . . . . . . . 191--195
David Callan Pair Them Up! A Visual Approach to the
Chung--Feller Theorem . . . . . . . . . 196--198
Lester H. Lange Did Plutarch Get Archimedes' Wishes
Right? . . . . . . . . . . . . . . . . . 199--204
L. F. Martins and
I. W. Rodrigues Angle Trisection by Fixed Point
Iteration . . . . . . . . . . . . . . . 205--208
David R. Guichard Sums of Selected Binomial Coefficients 209--213
Steven F. Bauman and
William O. Martin Assessing the Quantitative Skills of
College Juniors . . . . . . . . . . . . 214--220
Anonymous Fallacies, Flaws, and Flimflam . . . . . 221--222
M. Sayrafiezadeh A Generalization of the Mean Value
Theorem for Integrals . . . . . . . . . 223--224
Steve M. Cohen and
Paul R. Coe Card Shuffling in Discrete Mathematics 224--227
Mary Jean Winter Finding Volumes with the Definite
Integral: a Group Project . . . . . . . 227--228
Mark Schwartz The Chair, the Area Rug, and the Astroid 229--231
Jack Drucker Minimal Time of Descent . . . . . . . . 232--235
Larry Riddle Individualized Computer Investigations
for Multivariable Calculus . . . . . . . 235--237
Lawrence G. Gilligan Software Reviews . . . . . . . . . . . . 238--243
Anonymous Problems and Solutions . . . . . . . . . 244--250
Anonymous Media Highlights . . . . . . . . . . . . 251--258
Anonymous Editorial Board . . . . . . . . . . . . ??
Dean Clark and
E. R. Suryanarayan Inductive Tiling of the Plane by Penrose
Aperiodic Rhombi . . . . . . . . . . . . 266--267
Garret Sobczyk The Hyperbolic Number Plane . . . . . . 268--280
Ross A. Honsberger More Mathematical Gems . . . . . . . . . 281--283
Gerald Flynn Numerical Methods for Improper Integrals 284--291
William Staton and
Clifton Wingard Independent Sets and the Golden Ratio 292--296
Joseph B. Dence and
Thomas P. Dence A Surprise Regarding the Equation $ \phi
(x) = 2 (6 n + 1) $ . . . . . . . . . . 297--301
Anonymous Fallacies, Flaws, and Flimflam . . . . . 302--304
Dan Pritikin Rectangular-to-Polar Folding Fans . . . 305--308
E. Ray Bobo A Sequence Related to the Harmonic
Series . . . . . . . . . . . . . . . . . 308--310
Robert K. Stump A Normal Density Project . . . . . . . . 310--312
Howard Shaw Hyperbolic Functions and Proper Time in
Relativity . . . . . . . . . . . . . . . 312--315
Anonymous Computer Corner . . . . . . . . . . . . 316--316
Steven Schonefeld Eigenpictures: Picturing the Eigenvector
Problem . . . . . . . . . . . . . . . . 316--319
Michael G. Henle Software Reviews . . . . . . . . . . . . 320--328
Anonymous Problems and Solutions . . . . . . . . . 329--334
Harry Bixler Media Highlights . . . . . . . . . . . . 335--342
Anonymous Editorial Board . . . . . . . . . . . . ??
Shahar Boneh and
David C. Ogden A Combinatorial Queueing Model . . . . . 346--357
Daniel C. Isaksen Linear Algebra on the Gridiron . . . . . 358--360
Tilak de Alwis Projectile Motion with Arbitrary
Resistance . . . . . . . . . . . . . . . 361--367
Tommy Wright Pascal's Triangle Gets Its Genes from
Stirling Numbers of the First Kind . . . 368--371
Xuming Chen Recursive Formulas for $ \xi (2 k) $ and
$ L(2 k - 1) $ . . . . . . . . . . . . . 372--376
William G. Frederick and
James R. Hersberger The Mathematical Judge: a Fable . . . . 377--381
Anonymous Fallacies, Flaws, and Flimflam . . . . . 382--384
Timothy Murdoch Spherical Coordinates from Cylindrical
Coordinates on a Torus . . . . . . . . . 385--387
Eugene F. Schuster MAD Property of Medians: an Induction
Proof . . . . . . . . . . . . . . . . . 387--389
Jack E. Graver A Geometric Approach to Linear Functions 389--394
Jerome L. Lewis The Meeting of the Plows: a Simulation 395--400
David C. Arney and
Daniel J. Arney Software Reviews . . . . . . . . . . . . 401--403
Anonymous Acknowledgements . . . . . . . . . . . . 404--404
Anonymous Problems and Solutions . . . . . . . . . 405--410
Frank Swetz Media Highlights . . . . . . . . . . . . 411--418
Anonymous Editorial Board . . . . . . . . . . . . ??
Dan Kalman A Singularly Valuable Decomposition: The
SVD of a Matrix . . . . . . . . . . . . 2--23
Heinrich W. Guggenheimer Formulas of Linear Geometry . . . . . . 24--32
Stephen R. Cavior A Master Key for Ten Locks . . . . . . . 33--36
Leon Harkleroad How Mathematicians Know What Computers
Can't Do . . . . . . . . . . . . . . . . 37--42
Anonymous Fallacies, Flaws, and Flimflam . . . . . 43--46
John C. Hegarty Bond Duration: an Application of
Calculus . . . . . . . . . . . . . . . . 47--49
Paul Scholten and
Andrew Simoson The Falling Ladder Paradox . . . . . . . 49--54
Harold Reiter and
Isaac Sonin The ``Join the Club'' Interpretation of
Some Graph Algorithms . . . . . . . . . 54--58
Ralph P. Grimaldi and
Douglas R. Shier Redundancy and Reliability of
Communication Networks . . . . . . . . . 59--67
Jon Wilkin Software Reviews . . . . . . . . . . . . 68--73
Anonymous Problems and Solutions . . . . . . . . . 74--78
Anonymous Media Highlights . . . . . . . . . . . . 79--85
Anonymous Editorial Board . . . . . . . . . . . . ??
Javier Gomez-Calderon and
David M. Wells Why Polynomials Have Roots . . . . . . . 90--94
Joe F. Wampler and
Stephen E. Newman Integer Programming . . . . . . . . . . 95--100
Patrick J. Driscoll and
William P. Fox Presenting the Kuhn--Tucker Conditions
Using a Geometric Approach . . . . . . . 101--108
Dan Kalman Fractions with Cycling Digit Patterns 109--115
Anonymous Fallacies, Flaws, and Flimflam . . . . . 116--118
Michael C. Sullivan Knots about Stokes' Theorem . . . . . . 119--122
Jack Ryder Exploring Fibonacci Numbers Mod $M$ . . 122--124
Nishan Krikorian and
Mark Ramras Cubic Splines from Simpson's Rule . . . 124--126
Irl Bivens and
Stephen L. Davis Some Graphs Whose Vertices Pair Off by
Degree: Part I . . . . . . . . . . . . . 127--135
George Mackiw Computing in Abstract Algebra . . . . . 136--142
JoAnne Growney Geometry Class . . . . . . . . . . . . . 143--143
Alan T. Zehnder Software Reviews . . . . . . . . . . . . 144--148
Anonymous Problems and Solutions . . . . . . . . . 149--155
Peter Hilton Media Highlights . . . . . . . . . . . . 156--163
Anonymous Editorial Board . . . . . . . . . . . . ??
Raymond A. Beauregard and
E. R. Suryanarayan Pythagorean Triples: The Hyperbolic View 170--181
James R. Boone The Moise Plane . . . . . . . . . . . . 182--185
Ralph Howard and
Paul Sisson Capturing the Origin with Random Points:
Generalizations of a Putnam Problem . . 186--192
L. F. Martins and
I. W. Rodrigues A Serendipitous Encounter with the
Cantor Ternary Function . . . . . . . . 193--198
A. B. Urdaletova and
S. K. Kydyraliev Solving Linear Differential Equations by
Operator Factorization . . . . . . . . . 199--203
Anonymous Fallacies, Flaws, and Flimflam . . . . . 204--205
Jim Zeng A Note on the Brachistochrone Problem 206--208
David Olson Another Way to Graph a Sequence . . . . 208--209
Zhibo Chen Some Comments on ``Parametric Equations
and Plane Curves'' . . . . . . . . . . . 210--211
James L. Hartman A Terminally Discontinuous Function . . 211--212
Irl Bivens and
Stephen L. Davis Some Graphs Whose Vertices Pair Off by
Degree: Part II . . . . . . . . . . . . 213--219
Anonymous Computer Corner . . . . . . . . . . . . 220--220
Helen Skala Will the Real Best Fit Curve Please
Stand Up? . . . . . . . . . . . . . . . 220--223
Sally Fischbeck Software Reviews . . . . . . . . . . . . 224--230
Anonymous Problems and Solutions . . . . . . . . . 231--235
Anonymous Media Highlights . . . . . . . . . . . . 236--243
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers Still Questioning Authority: an
Interview with Jean Taylor . . . . . . . 250--266
Daniel C. Isaksen How to Kick a Field Goal . . . . . . . . 267--271
Robert E. Terrell Independence of Path and All That . . . 272--277
Felicia Moss Trachtenberg The Game of Dreidel Made Fair . . . . . 278--281
Anonymous Fallacies, Flaws, and Flimflam . . . . . 282--284
James C. Kirby Bargaining Theory, or Zeno's Used Cars 285--286
Robert L. Lamphere A Recurrence Relation in the Spinout
Puzzle . . . . . . . . . . . . . . . . . 286--289
David N. Adler Some Extensions of a Ubiquitous
Geometric Limit Problem . . . . . . . . 290--291
Elias Y. Deeba and
Dennis M. Rodriguez and
Ibrahim Wazir Critical Points of Polynomial Families 291--295
Joe Klerlein and
Scott Sportsman Generalizations of a Mathematical
Olympiad Problem . . . . . . . . . . . . 296--297
James A. Walsh Fractals in Linear Algebra . . . . . . . 298--304
Jerry Thornhill Software Reviews . . . . . . . . . . . . 305--311
Anonymous Problems and Solutions . . . . . . . . . 312--316
John A. Dossey Media Highlights . . . . . . . . . . . . 317--324
Anonymous Editorial Board . . . . . . . . . . . . ??
Chris Christensen Newton's Method for Resolving Affected
Equations . . . . . . . . . . . . . . . 330--340
George E. Andrews Mathematical Education: a Case for
Balance . . . . . . . . . . . . . . . . 341--348
David M. Mathews Mathematics Education: a Response to
Andrews . . . . . . . . . . . . . . . . 349--353
Anonymous George Andrews Replies . . . . . . . . . 354--355
Robert A. Fontenot Three Applications of a Familiar Formula 356--360
Mark Bridger Dynamic Function Visualization . . . . . 361--369
Anonymous Fallacies, Flaws, and Flimflam . . . . . 370--373
Gary D. White and
Kirby Smith The Rental Car Problem . . . . . . . . . 374--378
James Duemmel Complex Eigenvalues and Rotations: Are
Your Students Going in Circles? . . . . 378--381
Pat Touhey Countability via Bases Other Than 10 . . 382--384
John Nord and
Edward Miller Mercator's Rhumb Lines: a Multivariable
Application of Arc Length . . . . . . . 384--387
Robert Anschuetz II and
H. Sherwood When Is a Function's Inverse Equal to
Its Reciprocal? . . . . . . . . . . . . 388--393
Anonymous Computer Corner . . . . . . . . . . . . 394--394
Prashant S. Sansgiry and
Constance C. Edwards A Home Heating Model for Calculus
Students . . . . . . . . . . . . . . . . 394--397
L. Carl Leinbach Software Reviews . . . . . . . . . . . . 398--403
Anonymous Problems and Solutions . . . . . . . . . 404--409
Donald W. Bushaw Media Highlights . . . . . . . . . . . . 410--417
Anonymous Acknowledgments . . . . . . . . . . . . 418--418
Anonymous Editorial Board . . . . . . . . . . . . ??
Kevin G. Kirby Of Memories, Neurons, and Rank-One
Corrections . . . . . . . . . . . . . . 2--19
Chris Bernhardt and
Thomas Yuster Periodic Points of the Difference
Operator . . . . . . . . . . . . . . . . 20--26
Garret Sobczyk The Generalized Spectral Decomposition
of a Linear Operator . . . . . . . . . . 27--38
Ji Gao An Application of Elementary Geometry in
Functional Analysis . . . . . . . . . . 39--43
Anonymous Guidelines for Authors . . . . . . . . . 43--43
Anonymous Fallacies, Flaws, and Flimflam . . . . . 44--46
C. W. Groetsch Halley's Gunnery Rule . . . . . . . . . 47--50
Allen J. Schwenk Introduction to Limits, or Why Can't We
Just Trust the Table? . . . . . . . . . 51--51
Martha E. Dasef and
Steven M. Kautz Some Sums of Some Significance . . . . . 52--55
Melissa Shepard A Rose Is a Rose Is a Rose \ldots . . . 55--56
Jingcheng Tong Area and Perimeter, Volume and Surface
Area . . . . . . . . . . . . . . . . . . 57--57
Uwe F. Mayer A Proof That Polynomials Have Roots . . 58--58
Anonymous Computer Corner . . . . . . . . . . . . 59--59
Peter Zizler and
Holly Frase Eigenpictures and Singular Values of a
Matrix . . . . . . . . . . . . . . . . . 59--62
James P. Fink Software Reviews . . . . . . . . . . . . 63--66
Anonymous Problems and Solutions . . . . . . . . . 67--72
Anonymous Media Highlights . . . . . . . . . . . . 73--79
Anonymous Editorial Board . . . . . . . . . . . . ??
Bryan Dawson A Better Draft: Fair Division of the
Talent Pool . . . . . . . . . . . . . . 82--88
Kathie Yerion Gaussian Elimination and Dynamical
Systems . . . . . . . . . . . . . . . . 89--97
Temple H. Fay Harmonic Oscillators with Periodic
Forcing . . . . . . . . . . . . . . . . 98--105
Donald E. Hooley Using the College Mathematics Journal
Topic Index in Undergraduate Courses . . 106--109
William C. Mercier How Chaotic Things Work . . . . . . . . 110--118
Anonymous Fallacies, Flaws, and Flimflam . . . . . 119--121
Michael R. Cullen Cylinder and Cone Cutting . . . . . . . 122--123
Dale K. Hathaway and
Stephen L. Brown Fibonacci Powers and a Fascinating
Triangle . . . . . . . . . . . . . . . . 124--128
Helen Skala A Discover-$e$ . . . . . . . . . . . . . 128--129
Larry Hoehn A Concurrency Theorem and \em Geometer's
Sketchpad . . . . . . . . . . . . . . . 129--132
Anthony Lo Bello A Nod to Bertrand Russell . . . . . . . 133--133
Andrew Simoson An Envelope for a Spirograph . . . . . . 134--139
Angela C. Hare Software Reviews . . . . . . . . . . . . 140--144
Anonymous Problems and Solutions . . . . . . . . . 145--150
Anonymous Media Highlights . . . . . . . . . . . . 151--156
Anonymous Editorial Board . . . . . . . . . . . . ??
Stephen D. Abbott and
Matt Richey Take a Walk on the Boardwalk . . . . . . 162--171
Aimee Johnson and
Kathleen Madden Putting the Pieces Together:
Understanding Robinson's Nonperiodic
Tilings . . . . . . . . . . . . . . . . 172--181
Herbert R. Bailey and
Robert Bannister A Stronger Triangle Inequality . . . . . 182--186
Steven R. Dunbar The Average Distance Between Points in
Geometric Figures . . . . . . . . . . . 187--197
Anonymous Fallacies, Flaws, and Flimflam . . . . . 198--200
Bennett Eisenberg What Is the Margin of Error of a Poll? 201--203
Sahib Singh and
Dip Bhattacharya On Dividing Coconuts: a Linear
Diophantine Problem . . . . . . . . . . 203--204
Peter Schumer The Pen and the Barn . . . . . . . . . . 205--206
Richard E. Bayne and
James E. Joseph and
Myung H. Kwack and
Thomas H. Lawson Exploiting a Factorization of $ x^n -
y^n $ . . . . . . . . . . . . . . . . . 206--209
Michael W. Ecker Divergence of the Harmonic Series by
Rearrangement . . . . . . . . . . . . . 209--210
John Meier and
Jessica Wolfson Visualizing the Geometry of Lissajous
Knots . . . . . . . . . . . . . . . . . 211--216
William Mueller and
Richard Thompson Discovering Differential Equations in
Optics . . . . . . . . . . . . . . . . . 217--223
Carl Leinbach Software Reviews . . . . . . . . . . . . 224--230
Anonymous Problems and Solutions . . . . . . . . . 231--236
William Dunham Media Highlights . . . . . . . . . . . . 237--246
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers An Interview with Tom Apostol . . . . . 250--270
John S. Robertson Gudermann and the Simple Pendulum . . . 271--276
Brian J. Loe and
Nathaniel Beagley The Coffee Cup Caustic for Calculus
Students . . . . . . . . . . . . . . . . 277--284
Anonymous Fallacies, Flaws, and Flimflam . . . . . 285--287
Leonard Gillman Order Relations and a Proof of
l'Hôpital's Rule . . . . . . . . . . . . 288--292
Holly P. Hirst and
Wade T. Macey Bounding the Roots of Polynomials . . . 292--295
J. Marshall Ash Neither a Worst Convergent Series nor a
Best Divergent Series Exists . . . . . . 296--297
Russell Euler A Note on Taylor's Series for $ \sin (a
x + b) $ and $ \cos (a x + b) $ . . . . 297--298
Irl C. Bivens Multiple Derivatives of Compositions:
Investigating Some Special Cases . . . . 299--300
Paul Vodola Adventure Games, Permutations, and
Spreadsheets . . . . . . . . . . . . . . 301--309
Robert Mayes Software Reviews . . . . . . . . . . . . 310--314
Anonymous Problems and Solutions . . . . . . . . . 315--321
Philip D. Straffin Media Highlights . . . . . . . . . . . . 322--329
Anonymous Editorial Board . . . . . . . . . . . . ??
P. D. Barry On Arc Length . . . . . . . . . . . . . 338--347
Steven M. Hetzler A Continuous Version of Newton's Method 348--351
Paulo Ribenboim Are There Functions That Generate Prime
Numbers? . . . . . . . . . . . . . . . . 352--359
Underwood Dudley Is Mathematics Necessary? . . . . . . . 360--364
Mario Martelli and
Gerald Gannon Weighing Coins: Divide and Conquer to
Detect a Counterfeit . . . . . . . . . . 365--367
Rick Kreminski Using Simpson's Rule to Approximate Sums
of Infinite Series . . . . . . . . . . . 368--376
Anonymous Fallacies, Flaws, and Flimflam . . . . . 377--380
Anonymous Acknowledgments . . . . . . . . . . . . 380--380
Wolf von Rönik Doughnut Slicing . . . . . . . . . . . . 381--383
Allan A. Struthers Counterexamples to a Weakened Version of
the Two-Variable Second Derivative Test 383--385
Cathy Liebars Tying Up Loose Ends with Probability . . 386--388
William Barnier and
Douglas Martin Unifying a Family of Extrema Problems 388--391
Paul Eenigenburg A Note on the Ratio of Arc Length to
Chordal Length . . . . . . . . . . . . . 391--393
Anonymous Computer Corner . . . . . . . . . . . . 394--394
Richard A. Jacobson Paths of Minimum Length in a Regular
Tetrahedron . . . . . . . . . . . . . . 394--397
Michael Frame Software Reviews . . . . . . . . . . . . 398--405
Anonymous Problems and Solutions . . . . . . . . . 406--411
Anonymous Media Highlights . . . . . . . . . . . . 412--419
Anonymous Editorial Board . . . . . . . . . . . . ??
David D. Bleecker and
Lawrence J. Wallen The World's Biggest Taco . . . . . . . . 2--12
Raymond A. Beauregard and
E. R. Suryanarayan The Brahmagupta Triangles . . . . . . . 13--17
Federico Fernández A Class of Pleasing Periodic Designs . . 18--26
Joan R. Hundhausen Zeroing In on the Delta Function . . . . 27--33
Anonymous Fallacies, Flaws, and Flimflam . . . . . 34--36
Eugene C. Boman and
Margaret A. Misconish A Diagonal Perspective on Matrices . . . 37--38
Yong-Zhuo Chen and
Richard F. Melka Finding a Determinant and Inverse Matrix
by Bordering . . . . . . . . . . . . . . 38--39
Bettina Richmond and
Tom Richmond Characterizing Power Functions by
Volumes of Revolution . . . . . . . . . 40--41
Richard Johnsonbaugh and
Duane W. DeTemple A Discrete Intermediate Value Theorem 42--42
Duane W. DeTemple Colored Polygon Triangulations . . . . . 43--47
Richard B. Thompson Designing a Baseball Cover . . . . . . . 48--61
Jon Wilkin Software Reviews . . . . . . . . . . . . 62--65
Anonymous Problems and Solutions . . . . . . . . . 66--72
Reuben Hersh Media Highlights . . . . . . . . . . . . 73--80
Anonymous Editorial Board . . . . . . . . . . . . ??
Donald J. Albers An Interview with Lars V. Ahlfors . . . 82--92
Alexander J. Hahn Two Historical Applications of Calculus 93--103
Steven Wilkinson Numerically Parametrizing Curves . . . . 104--119
David M. Bloom Singles in a Sequence of Coin Tosses . . 120--127
Thomas Hern and
Cliff Long and
Andy Long Looking at Order of Integration and a
Minimal Surface . . . . . . . . . . . . 128--133
Anonymous Fallacies, Flaws, and Flimflam . . . . . 134--136
Leonard Gillman Revisiting Arc Length . . . . . . . . . 137--138
James E. Mann, Jr. The Buckled Rail: Three Formulations . . 138--141
Viet Ngo and
Saleem Watson Who Cares If $ X^2 $ + 1 = 0 Has a
Solution? . . . . . . . . . . . . . . . 141--144
Cheng-Shyong Lee Polishing the Star . . . . . . . . . . . 144--145
David Callan When Is ``Rank'' Additive? . . . . . . . 145--147
Anonymous Computer Corner . . . . . . . . . . . . 148--148
Charles R. Johnson and
Brenda K. Kroschel Clock Hands Pictures for $ 2 \times 2 $
Real Matrices . . . . . . . . . . . . . 148--150
Sergey Markelov Geometric Characterization of the
Shortest Path in a Tetrahedron . . . . . 150--151
Anonymous Problems and Solutions . . . . . . . . . 152--157
Anonymous Media Highlights . . . . . . . . . . . . 158--165
Anonymous Editorial Board . . . . . . . . . . . . ??
Daniel Pedoe In Love with Geometry . . . . . . . . . 170--188
Aaron Klebanoff and
John Rickert Studying the Cantor Dust at the Edge of
Feigenbaum Diagrams . . . . . . . . . . 189--198
Colm Mulcahy and
John Rossi A Fresh Approach to the Singular Value
Decomposition . . . . . . . . . . . . . 199--207
Arie Bialostocki An Application of Elementary Group
Theory to Central Solitaire . . . . . . 208--212
Jean-Claude Derderian and
Enriqueta Rodríguez-Carrington Undersampled Sine Waves . . . . . . . . 213--218
Peter D. Lax Fallacies, Flaws, And Flimflam . . . . . 219--221
Min Deng and
Mary T. Whalen The Mathematics of Cootie . . . . . . . 222--224
Michael Scott McClendon Minimal Pyramids . . . . . . . . . . . . 224--226
Mike O'Leary Taylor Polynomials for Rational
Functions . . . . . . . . . . . . . . . 226--228
Michael J. Seery Pursuit and Regular $N$-gons . . . . . . 228--229
Anne M. Burns Modeling Trees with a Stochastic Matrix 230--236
William C. Bauldry Software Reviews . . . . . . . . . . . . 237--241
Anonymous Problems and Solutions . . . . . . . . . 242--248
Daniel E. Otero Media Highlights . . . . . . . . . . . . 249--256
Anonymous Editorial Board . . . . . . . . . . . . ??
Stephen Wirkus and
Richard Rand and
Andy Ruina How to Pump a Swing . . . . . . . . . . 266--275
Michael D. Hirschhorn The Fundamental Theorem of Algebra . . . 276--277
James W. Daniel How Much Money Do You (or Your Parents)
Need for Retirement? . . . . . . . . . . 278--283
Charles Jepsen and
Roc Yang Making Squares from Pythagorean
Triangles . . . . . . . . . . . . . . . 284--288
Vincent Lucarelli On Factoring n with the b-algorithm . . 289--295
Premchand Anne Egyptian Fractions and the Inheritance
Problem . . . . . . . . . . . . . . . . 296--300
Anonymous Fallacies, Flaws, and Flimflam . . . . . 301--303
Michael A. Carchidi Generating Exotic-Looking Vector Spaces 304--308
Norton Starr Nothing Counts for Something . . . . . . 308--309
Yukio Kobayashi A Geometric View of a Vector Identity 309--310
Bob Palais An Example Demonstrating the Fundamental
Theorem of Calculus . . . . . . . . . . 311--312
Sidney H. Kung More Coconuts . . . . . . . . . . . . . 312--313
Larry Riddle Arc Length Contest . . . . . . . . . . . 314--320
Van Bain \em Classroom Computer Capsule: An
Algorithm for Drawing the $n$-Cube . . . 320--322
Steven Wilkinson Software Reviews . . . . . . . . . . . . 323--329
Anonymous Problems and Solutions . . . . . . . . . 330--336
Jean Pedersen Media Highlights . . . . . . . . . . . . 337--344
Anonymous Editorial Board . . . . . . . . . . . . ??
Brian J. McCartin Prelude to Musical Geometry . . . . . . 354--370
Luiz Felipe Martins A Simple Decision Rule for a Guessing
Game . . . . . . . . . . . . . . . . . . 371--375
Ethan Berkove and
Rich Marchand The Long Arm of Calculus . . . . . . . . 376--386
Frank Zizza Differential Forms for Constrained
Max-Min Problems: Eliminating Lagrange
Multipliers . . . . . . . . . . . . . . 387--396
Donald A. Teets and
Karen Whitehead Computation of Planetary Orbits . . . . 397--404
Anonymous Fallacies, Flaws, and Flimflam . . . . . 405--407
J. B. Thoo A Picture Is Worth a Thousand Words . . 408--411
Bennett Eisenberg How Much Should You Pay for a
Derivative? . . . . . . . . . . . . . . 412--414
Saad M. Adnan Candies and Dollars . . . . . . . . . . 414--415
Dan Kalman and
James White A Simple Solution of the Cubic . . . . . 415--418
Marc D. Sanders and
Barry A. Tesman MATH and Other Four-Letter Words . . . . 418--419
Michael W. Ecker A Novel Approach to Geometric Series . . 419--420
Milton P. Eisner The Probability of Passing a
Multiple-Choice Test . . . . . . . . . . 421--426
Elly Claus-McGahan Software Reviews . . . . . . . . . . . . 427--433
Anonymous Problems and Solutions . . . . . . . . . 434--440
Bruce Berndt Media Highlights . . . . . . . . . . . . 441--448
Anonymous Editorial Board . . . . . . . . . . . . ??
Clifford H. Wagner Coming to America: The Journey of an
Immigrant Scholar . . . . . . . . . . . 2--17
Martin Gardner The Asymmetric Propeller . . . . . . . . 18--22
Khristo N. Boyadzhiev Spirals and Conchospirals in the Flight
of Insects . . . . . . . . . . . . . . . 23--31
Paul M. Sommers Student's $t$ and Crackers . . . . . . . 32--34
Julian F. Fleron Gabriel's Wedding Cake . . . . . . . . . 35--38
Anonymous Fallacies, Flaws, and Flimflam . . . . . 39--43
Ze-Li Dou and
Susan G. Staples Maximizing the Arclength in the
Cannonball Problem . . . . . . . . . . . 44--45
Keith Kendig Pictures Suggest How to Improve
Elementary Numerical Integration . . . . 45--50
Jeff Suzuki Multiplying and Dividing Polynomials
Using Geloxia . . . . . . . . . . . . . 50--53
Jon Wilkin Software Reviews . . . . . . . . . . . . 54--59
Anonymous Problems and Solutions . . . . . . . . . 60--66
John Fossa Letter to the Editor . . . . . . . . . . 67--68
Anonymous Media Highlights . . . . . . . . . . . . 69--76
Anita E. Solow Book Review . . . . . . . . . . . . . . 77--80
Anonymous Editorial Board . . . . . . . . . . . . ??
Ezra Brown Square Roots from 1; 24, 51, 10 to Dan
Shanks . . . . . . . . . . . . . . . . . 82--95
Hardy Grant Mathematics and The Liberal Arts . . . . 96--105
James Case Interval Arithmetic and Analysis . . . . 106--111
Allen J. Schwenk \em Several Sets of n + 1 \em Shapes,
Each the Similitude Union of the Other n 112--117
Hidefumi Katsuura From Euler to Fermat . . . . . . . . . . 118--119
Thomas G. Edwards and
Lawrence Brenton An Attempt to Foster Students'
Construction of Knowledge During a
Semester Course in Abstract Algebra . . 120--128
Anonymous Fallacies, Flaws, and Flimflam . . . . . 129--132
Michael J. Bradley and
Michael St. Vincent and
David L. Finn Additivity $ \oplus $ Homogeneity . . . 133--135
Scott E. Brodie On ``Rethinking Rigor in Calculus
\ldots,'' or Why We Don't Do Calculus on
the Rational Numbers . . . . . . . . . . 135--138
Kil S. Lee A Far-reaching Formula . . . . . . . . . 138--140
James Chappell and
Thomas J. Osler The Trinomial Triangle . . . . . . . . . 141--142
Anonymous Problems and Solutions . . . . . . . . . 143--148
Anonymous Media Highlights . . . . . . . . . . . . 149--158
John Ewing Book Review . . . . . . . . . . . . . . 159--161
Anonymous Editorial Board . . . . . . . . . . . . ??
Peter Hilton and
Jean Pedersen Relating Geometry and Algebra in the
Pascal Triangle, Hexagon, Tetrahedron,
and Cuboctahedron Part I: Binomial
Coefficients, Extended Binomial
Coefficients and Preparation for Further
Work . . . . . . . . . . . . . . . . . . 170--186
Todd G. Will The Bus Driver's Sanity Problem . . . . 187--194
Pawel Strzelecki and
Abe Shenitzer Continuous Versions of the (Dirichlet)
Drawer Principle . . . . . . . . . . . . 195--196
Hardy Grant Mathematics and the Liberal Arts-II . . 197--203
Brian C. Fowler and
Randall J. Swift Relabeling Dice . . . . . . . . . . . . 204--208
Anonymous Fallacies, Flaws, and Flimflam . . . . . 209--211
Michel Bataille and
Guanshen Ren Construction without Words: Focus and
Directrix . . . . . . . . . . . . . . . 212--212
Kurt Cogswell Computers and Advanced Mathematics in
the Calculus Classroom . . . . . . . . . 213--216
Stephen Kenton A Natural Proof of the Chain Rule . . . 216--218
David L. Deever The Average Distance of the Earth from
the Sun . . . . . . . . . . . . . . . . 218--220
Mark Schwartz and
Darryl Adams Shortest Path Solution by Epitrochoid
Machine . . . . . . . . . . . . . . . . 221--225
Geza Schay Using Consistency Conditions to Solve
Linear Systems . . . . . . . . . . . . . 226--229
Anonymous Problems and Solutions . . . . . . . . . 230--235
Anonymous Media Highlights . . . . . . . . . . . . 236--243
Stan Kelly-Boode Book Review . . . . . . . . . . . . . . 244--247
Anonymous Editorial Board . . . . . . . . . . . . ??
S. I. B. Gray and
Tagui Malakyan The Witch of Agnesi: a Lasting
Contribution from the First Surviving
Mathematical Work Written by a Woman . . 258--268
John A. Knox and
Harlan J. Brothers Novel Series-based Approximations to $e$ 269--275
Dennis Connolly Casino Gambling, the Ultimate Strategy 276--278
Peter Hilton and
Jean Pedersen Relating Geometry and Algebra in the
Pascal Triangle, Hexagon, Tetrahedron,
and Cuboctahedron Part II: Geometry and
Algebra in Higher Dimensions:
Identifying the Pascal Cuboctahedron . . 279--292
Robert J. Wisner Powers as Uniform Sums of Positive
Squares . . . . . . . . . . . . . . . . 293--296
Allan J. Rossman and
Beth L. Chance Teaching the Reasoning of Statistical
Inference: a ``Top Ten'' List . . . . . 297--305
Anonymous Fallacies, Flaws, and Flimflam . . . . . 306--308
Frank Burk Natural Logarithms via Long Division . . 309--311
Raymond Boute Simple Geometric Solutions to De
l'Hospital's Pulley Problem . . . . . . 311--314
Selvaratnam Sridharma The Derivative of $ \Sin \theta $ . . . 314--315
Haris Tabakovic and
Joseph Paullet and
Richard Bertram Measuring the Curl of Paper . . . . . . 315--317
Anonymous Problems and Solutions . . . . . . . . . 318--323
Anonymous Miscellanea . . . . . . . . . . . . . . 324--328
Anonymous Media Highlights . . . . . . . . . . . . 329--337
Anonymous Editorial Board . . . . . . . . . . . . ??
Dan Kennedy Things I Have Learned at the AP Reading 346--355
Robert Barrington Leigh and
Richard Travis Ng Minimizing Aroma Loss . . . . . . . . . 356--358
Arthur T. Benjamin and
Jennifer J. Quinn Recounting Fibonacci and Lucas
Identities . . . . . . . . . . . . . . . 359--366
Robert Fakler Do Most Cubic Graphs Have Two Turning
Points? . . . . . . . . . . . . . . . . 367--369
Charles Waiveris and
Yuanqian Chen Folding Stars . . . . . . . . . . . . . 370--378
K. E. Clark and
S. Hill The Effects of a Stiffening Spring . . . 379--382
Anonymous Fallacies, Flaws, and Flimflam . . . . . 383--386
W. M. Priestley From Square Roots to $n$-th Roots:
Newton's Method in Disguise . . . . . . 387--388
Richard E. Klima and
Robert G. Donnelly Amortization: an Application of Calculus 388--391
Paul Cella Reexamining the Catenary . . . . . . . . 391--393
Joseph J. Roseman and
Gideon Zwas Second Order Iterations . . . . . . . . 393--396
Marc Chamberland The Series for $e$ via Integration . . . 397--397
Dan Kalman Software Reviews . . . . . . . . . . . . 398--405
Anonymous Problems and Solutions . . . . . . . . . 406--412
Anonymous Media Highlights . . . . . . . . . . . . 413--421
Anonymous Miscellanea . . . . . . . . . . . . . . 422--424
Mark Saul Book Review . . . . . . . . . . . . . . 425--428
Anonymous Editorial Board . . . . . . . . . . . . ??
Chip Ross and
Jody Sorensen Will the Real Bifurcation Diagram Please
Stand Up! . . . . . . . . . . . . . . . 2--14
Robert A. Bosch Optimal Card-Collecting Strategies for
Magic: The Gathering . . . . . . . . . . 15--21
Patricia R. Allaire and
Antonella Cupillari Artemas Martin: an Amateur Mathematician
of the Nineteenth Century and His
Contribution to Mathematics . . . . . . 22--34
L. Grove and
O. Yiparaki Contumacious Spheres . . . . . . . . . . 35--41
David Calvis Partially Differentiable, Yes;
Continuous, No . . . . . . . . . . . . . 42--47
Theodore G. Ammon Fallacies, Flaws, and Flimflam . . . . . 48--49
Colonel Johnson, Jr. Group Operation Tables and Normalizers 50--51
Peter Thompson and
Lorrie Lendvoy Getting Normal Probability
Approximations without Using Normal
Tables . . . . . . . . . . . . . . . . . 51--54
Kirby C. Smith Normal Lines and Curvature . . . . . . . 54--56
Paul Fjelstad and
Peter Hammer A Picture for Real Arithmetic . . . . . 56--60
Joseph Wiener Integrals of $ \cos^{2 n} X $ and $
\sin^{2 n} X $ . . . . . . . . . . . . . 60--61
Anonymous Problems and Solutions . . . . . . . . . 62--67
Anonymous Miscellanea . . . . . . . . . . . . . . 68--68
Anonymous Media Highlights . . . . . . . . . . . . 69--76
Carl Linderholm Book Review . . . . . . . . . . . . . . 77--79
Anonymous Editorial Board . . . . . . . . . . . . ??
Marcia Kleinz and
Thomas J. Osler A Child's Garden of Fractional
Derivatives . . . . . . . . . . . . . . 82--88
Hans Walser The Pop-up Cuboctahedron . . . . . . . . 89--92
John D. Lorch Modeling the Gaitpath of a Running
Animal . . . . . . . . . . . . . . . . . 93--97
Peter W. Wade and
William R. Wade Recursions That Produce Pythagorean
Triples . . . . . . . . . . . . . . . . 98--101
C. L. Adler and
James Tanton $ \pi $ is the Minimum Value for Pi . . 102--106
Bobette Hayden Thorsen The Eigenvalues of an Infinite Matrix 107--110
Raymond A. Beauregard and
E. R. Suryanarayan General Arithmetic Triangles and
Bhaskara's Equation . . . . . . . . . . 111--115
S. A. Fulling Related Rates Collide with Vectors . . . 116--119
Shay Gueron Fallacies, Flaws, and Flimflam . . . . . 120--123
Arthur T. Benjamin and
Matthew T. Fluet A Rational Solution to Cootie . . . . . 124--125
Michael D. Hirschhorn More on COOTIE . . . . . . . . . . . . . 126--128
Mark Krusemeyer An ``Extremely'' Cautionary Tale . . . . 128--130
Arthur C. Segal A Quick Construction of Tangents to an
Ellipse . . . . . . . . . . . . . . . . 131--131
Jack E. Graver and
Lawrence J. Lardy Linear Functions and Rounding . . . . . 132--136
Anonymous Problems and Solutions . . . . . . . . . 137--143
Antonella Cupillari Miscellanea . . . . . . . . . . . . . . 144--147
Anonymous Media Highlights . . . . . . . . . . . . 148--156
Michael A. McDonald Book Review . . . . . . . . . . . . . . 157--159
Anonymous Editorial Board . . . . . . . . . . . . ??
Ezra Brown Three Fermat Trails to Elliptic Curves 162--172
Martin Gardner Modeling Mathematics With Playing Cards 173--177
Frank Burk Summing Series via Integrals . . . . . . 178--181
Paulus Gerdes On Lunda-designs and the Construction of
Associated Magic Squares of Order $ 4 p
$ . . . . . . . . . . . . . . . . . . . 182--188
Paul M. Sommers The Super Bowl Theory: Fourth and Long 189--192
Patricia Clark Kenschaft 455 Mathematics Majors: What Have They
Done Since? . . . . . . . . . . . . . . 193--199
David L. Farnsworth The Geometry of Statistics . . . . . . . 200--204
Shay Gueron Fallacies, Flaws, and Flimflam . . . . . 205--207
Stewart Venit and
Richard Katz Eigenvalues of Matrices of Low Rank . . 208--210
Thomas J. Osler Binomials to Binomials . . . . . . . . . 211--212
Jessica Benashaski and
John Meier and
Kevin O'Brien and
Paige Reinheimer and
Margaret Skarbek Introducing Hyperbolicity via Piecewise
Euclidean Complexes . . . . . . . . . . 213--217
Neil Eklund $t$-Probabilities as Finite Sums . . . . 217--218
Anonymous Problems and Solutions . . . . . . . . . 219--226
Anonymous Media Highlights . . . . . . . . . . . . 227--235
Anonymous Miscellanea . . . . . . . . . . . . . . 236--239
Peter Ross Book Review . . . . . . . . . . . . . . 240--244
Anonymous Editorial Board . . . . . . . . . . . . ??
Bret Draayer $N$-Site Insights . . . . . . . . . . . 250--258
Brian E. Smith and
Francis J. Merceret The Lognormal Distribution . . . . . . . 259--261
Hugh Thurston Can We Improve the Teaching of Calculus? 262--267
Thomas E. Bradstreet Food and Drug Interaction: What Role
Does Statistics Play? . . . . . . . . . 268--273
Martin Gardner Some New Results on Magic Hexagrams . . 274--280
D. A. Linwood The Calculus and Gamow's Theory of
Gravitation . . . . . . . . . . . . . . 281--285
Bruce Hedman Colin Maclaurin's Quaint Word Problems 286--289
Roman W. Wong The Orbits of a Unimodular Affine
Transformation . . . . . . . . . . . . . 290--296
Donald E. Hooley Collapsed Matrices with (Almost) the
Same Eigenstuff . . . . . . . . . . . . 297--299
James R. Hughes Applications of Fourier Series in
Classical Guitar Technique . . . . . . . 300--303
Andrew Simoson Fast-Food-Frusta and the Center of
Gravity . . . . . . . . . . . . . . . . 303--306
Donald A. Teets Fallacies, Flaws, and Flimflam . . . . . 307--309
Anonymous Software Reviews . . . . . . . . . . . . 310--313
Anonymous Problems and Solutions . . . . . . . . . 314--320
Anonymous Media Highlights . . . . . . . . . . . . 321--328
Bo Green A Project for Discovery, Extension, and
Generalization in Abstract Algebra . . . 329--332
Anonymous Editorial Board . . . . . . . . . . . . ??
L. D. Humphreys and
R. Shammas Finding Unpredictable Behavior in a
Simple Ordinary Differential Equation 338--346
Gillian Saenz and
Christopher Jackson and
Ryan Crumley The Asymmetric Propeller Revisited . . . 347--349
Herb Bailey and
Yanir A. Rubinstein A Variety of Triangle Inequalities . . . 350--355
Richard Iltis Runs With No Winner in a Lottery . . . . 356--361
Peter Y. Woo Straightedge Constructions, Given a
Parabola . . . . . . . . . . . . . . . . 362--372
Al Cuoco Meta-Problems in Mathematics . . . . . . 373--378
Timothy G. Feeman and
Osvaldo Marrero Sequences of Chords and of Parabolic
Segments Enclosing Proportional Areas 379--382
Hans Walser The Pascal Pyramid . . . . . . . . . . . 383--392
Anonymous Fallacies, Flaws, and Flimflam . . . . . 393--396
David Sanchez and
Kirby C. Smith Normal Lines and the Evolute Curve . . . 397--403
Allen J. Schwenk A Polynomial with a Root Mod $m$ for
Every $m$ . . . . . . . . . . . . . . . 403--405
H. Azad and
A. Laradji On a Theorem of Clay . . . . . . . . . . 405--406
Jorge Aarão Tangents without Calculus . . . . . . . 406--407
Anonymous Problems and Solutions . . . . . . . . . 408--414
Anonymous Media Highlights . . . . . . . . . . . . 415--420
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Dan Kalman A Generalized Logarithm for
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W. D. Kaigh The Case of the Missing Lottery Number 15--19
Andrew E. Long and
Clifford A. Long Surface Approximation and Interpolation
via Matrix SVD . . . . . . . . . . . . . 20--25
Michael A. Aaron and
Brewster B. Boyd, Jr. and
Melanie J. Curtis and
Paul M. Sommers Punxsutawney's Phenomenal Phorecaster 26--29
Yves Nievergelt Well-Rounded Figures . . . . . . . . . . 30--32
Shay Gueron Speeding Up a Numerical Algorithm . . . 33--38
Martin Gardner Against the Odds . . . . . . . . . . . . 39--43
Bill Goldbloom Bloch Tension in Generalized Geometric
Sequences . . . . . . . . . . . . . . . 44--47
Anonymous Fallacies, Flaws, and Flimflam . . . . . 48--51
Anonymous Classroom Capsules . . . . . . . . . . . 52--53
Anonymous Problems and Solutions . . . . . . . . . 60--67
Anonymous Miscellanea . . . . . . . . . . . . . . 68--71
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Randall McCutcheon Analyzing Games of Information . . . . . 82--90
R. S. Pinkham Simpson's Rule with Constant Weights . . 91--93
David M. Bradley Verhulst's Logistic Curve . . . . . . . 94--98
Bronislaw Czarnocha and
Ed Dubinsky and
Sergio Loch and
Vrunda Prabhu and
Draga Vidakovic Conceptions of Area: In Students and in
History . . . . . . . . . . . . . . . . 99--109
Junpei Sekino The Band Around a Convex Set . . . . . . 110--114
Anonymous Fallacies, Flaws, and Flimplam . . . . . 115--118
Anonymous Classroom Capsules . . . . . . . . . . . 119--137
Anonymous Software Reviews . . . . . . . . . . . . 138--140
Anonymous Problems and Solutions . . . . . . . . . 141--146
Anonymous Media Highlights . . . . . . . . . . . . 147--154
Brian Blank Book Review . . . . . . . . . . . . . . 155--160
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Jane M. Day and
Dan Kalman Teaching Linear Algebra: Issues and
Resources . . . . . . . . . . . . . . . 162--168
Larry Clevenson and
Mark F. Schilling and
Ann E. Watkins and
William Watkins The Average Speed on the Highway . . . . 169--171
Tom M. Apostol and
Mamikon A. Mnatsakanian Good Rational Approximations to
Logarithms . . . . . . . . . . . . . . . 172--179
Joseph Wiener Differentiation with Respect to a
Parameter . . . . . . . . . . . . . . . 180--184
John A. Fossa and
Glenn W. Erickson The Lord Over Better and Worse Births 185--193
Mikko Stenlund On the Tangent Lines of a Parabola . . . 194--196
Anonymous Fallacies, Flaws, and Flimflam . . . . . 197--200
Anonymous Classroom Capsules . . . . . . . . . . . 201--210
Anonymous Problems and Solutions . . . . . . . . . 211--217
Marcia Tharp Software Reviews . . . . . . . . . . . . 218--222
Anonymous Media Highlights . . . . . . . . . . . . 223--231
Steven G. Krantz Book Review . . . . . . . . . . . . . . 232--237
Anonymous Miscellanea . . . . . . . . . . . . . . 238--240
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James Tattersall and
Shawnee McMurran An Interview with Dame Mary L.
Cartwright, D.B.E., F.R.S. . . . . . . . 242--254
Louis Bragg Arctangent Sums . . . . . . . . . . . . 255--257
Elizabeth B. Appelbaum Models for Growth . . . . . . . . . . . 258--259
Ezra Brown Magic Squares, Finite Planes, and Points
of Inflection on Elliptic Curves . . . . 260--267
Noah Samuel Brannen The Sun, the Moon, and Convexity . . . . 268--272
Scott J. Beslin and
Douglas J. Baney Another Look at Factoring Polynomials 273--275
Maria Cecília K. Aguilera-Navarro and
Valdir C. Aguilera-Navarro and
Ricardo C. Ferreira and
Neuza Teramon Rational Approximations to Power
Expansions . . . . . . . . . . . . . . . 276--278
Anonymous Fallacies, Flaws, and Flimflam . . . . . 279--282
Anonymous Classroom Capsules . . . . . . . . . . . 283--296
Anonymous Problems and Solutions . . . . . . . . . 297--303
Anonymous Media Highlights . . . . . . . . . . . . 304--313
Patricia Clark Kenschaft Book Review . . . . . . . . . . . . . . 314--316
Anonymous Miscellanea . . . . . . . . . . . . . . 317--318
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Ira Rosenholtz Estimating Large Integrals: The Bigger
They Are, The Harder They Fall . . . . . 322--329
Neil Eklund CORDIC: Elementary Function Computation
Using Recursive Sequences . . . . . . . 330--333
Timothy G. Feeman Conformality, the Exponential Function,
and World Map Projections . . . . . . . 334--342
Andy Liu In Search of a Missing Link: a Case
Study in Error-Correcting Codes . . . . 343--347
Wolf von Rönik The Profit In Being Unbalanced . . . . . 348--351
Pam Littleton and
David A. Sánchez Dipsticks for Cylindrical Storage
Tanks-Exact and Approximate . . . . . . 352--358
Michael Strizhevsky and
Dmitry Kreslavskiy Geometric Progressions --- a Geometric
Approach . . . . . . . . . . . . . . . . 359--362
Anonymous Fallacies, Flaws, and Flimflam . . . . . 363--368
Anonymous Classroom Capsules . . . . . . . . . . . 369--380
Anonymous Problems and Solutions . . . . . . . . . 381--387
Anonymous Student Research Projects . . . . . . . 388--393
Anonymous Media Highlights . . . . . . . . . . . . 394--401
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David Bressoud Was Calculus Invented In India? . . . . 2--13
Paul M. Sommers Is Presidential Greatness Related to
Height? . . . . . . . . . . . . . . . . 14--16
J. G. Simmonds Perfecting the Analog of a Deck of Cards
or Why Evolution Can't Be Left to Chance 17--20
Ioana Mihaila Cantor, 1 /4, and its Family and Friends 21--23
Jim Sauerberg and
Alan Tarr Centering . . . . . . . . . . . . . . . 24--31
Stephen B. Maurer Hat Derivatives . . . . . . . . . . . . 32--37
Anonymous Fallacies, Flaws, and Flimflam . . . . . 38--41
Anonymous Classroom Capsules . . . . . . . . . . . 42--53
Anonymous Problems and Solutions . . . . . . . . . 54--59
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Frank Swetz Book Review . . . . . . . . . . . . . . 69--70
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Monte J. Zerger A Visit With Six . . . . . . . . . . . . 74--87
Herb Bailey On Running in the Rain . . . . . . . . . 88--92
sarah-marie belcastro and
Thomas C. Hull Classifying Frieze Patterns Without
Using Groups . . . . . . . . . . . . . . 93--98
Thomas J. Osler and
Marcus Wright A Tale of Two Series . . . . . . . . . . 99--106
Leigh Atkinson Where Do Functions Come From? . . . . . 107--112
Philip K. Hotchkiss It's Perfectly Rational . . . . . . . . 113--117
Bonnie Shulman Is There Enough Poison Gas to Kill the
City?: The Teaching of Ethics in
Mathematics Classes . . . . . . . . . . 118--125
Asuman Aksoy and
Mario Martelli Mixed Partial Derivatives and Fubini's
Theorem . . . . . . . . . . . . . . . . 126--130
Tom Farmer Designing a Calculus Mobile . . . . . . 131--136
Anonymous Fallacies, Flaws, and Flimflam . . . . . 137--139
Anonymous Classroom Capsules . . . . . . . . . . . 140--149
Anonymous Problems and Solutions . . . . . . . . . 150--156
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James J. Tattersall An Interview with Dirk Struik on the Eve
of His One Hundredth Birthday . . . . . 178--187
Richard K. Guy and
Marc M. Paulhus Nine Cubits or Simple Soma . . . . . . . 188--195
Christopher Moretti Moving a Couch Around a Corner . . . . . 196--200
Jeanne Albert Sums of Uniformly Distributed Variables:
a Combinatorial Approach . . . . . . . . 201--206
Reuben Hersh The ``Origin'' of Geometry . . . . . . . 207--211
Raymond A. Beauregard and
E. R. Suryanarayan A Ramanujan Result Viewed From Matrix
Algebra . . . . . . . . . . . . . . . . 212--214
Keith A. Willoughby Winning Games in Canadian Football: a
Logistic Regression Analysis . . . . . . 215--220
Nathan D. Cahill and
John R. D'Errico and
Darren A. Narayan and
Jack Y. Narayan Fibonacci Determinants . . . . . . . . . 221--225
Anonymous Fallacies, Flaws, and Flimflam . . . . . 226--229
Anonymous Classroom Capsules . . . . . . . . . . . 230--239
Anonymous Problems and Solutions . . . . . . . . . 240--246
Anonymous Media Highlights . . . . . . . . . . . . 247--255
Peter Ross Book Review . . . . . . . . . . . . . . 256--259
Anonymous Editorial Board . . . . . . . . . . . . ??
Edward Sandifer Spanish Colonial Mathematics: a Window
on the Past . . . . . . . . . . . . . . 266--278
Fredric T. Howard A Generalized Chinese Remainder Theorem 279--282
David L. Finn Can a Bicycle Create a Unicycle Track? 283--292
Steven P. Bisgaier and
Benjamin S. Bradley and
Peter D. Harwood and
Paul M. Sommers Chasing Hank Aaron's Home Run Record . . 293--295
Eugene Boman and
Frank Uhlig When $ 1 / (a + b) = 1 / a + 1 / b $,
Anyway? . . . . . . . . . . . . . . . . 296--300
David B. Agard and
Michael W. Shackleford A New Look at the Probabilities in Bingo 301--305
Howard W. Eves A Very Brief History of Statistics . . . 306--308
Anonymous Fallacies, Flaws, and Flimflam . . . . . 309--312
Anonymous Classroom Capsules . . . . . . . . . . . 313--324
Anonymous Problems and Solutions . . . . . . . . . 325--331
Anonymous Media Highlights . . . . . . . . . . . . 332--340
Jet Wimp Book Review . . . . . . . . . . . . . . 341--344
Anonymous Miscellanea . . . . . . . . . . . . . . 345--352
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Robin Wilson Alice in Numberland --- an Informal
Dramatic Presentation in 8 Fits . . . . 354--377
Richard F. McCoart Lewis Carroll's Amazing Number-Guessing
Game . . . . . . . . . . . . . . . . . . 378--383
Dan Kalman An Underdetermined Linear System for GPS 384--390
Geoffrey C. Berresford Runs in Coin Tossing: Randomness
Revealed . . . . . . . . . . . . . . . . 391--394
Anonymous Fallacies, Flaws, and Flimflam . . . . . 395--398
Anonymous Classroom Capsules . . . . . . . . . . . 399--400
Anonymous Problems and Solutions . . . . . . . . . 410--416
Anonymous Media Highlights . . . . . . . . . . . . 417--425
Jonathan Lewin Software Reviews . . . . . . . . . . . . 426--430
Anonymous Miscellanea . . . . . . . . . . . . . . 431--432
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Michael G. Neubauer and
Joel Zeitlin Apportionment and the 2000 Election . . 2--10
Thomas C. McMillan Examining Continuity, Partial
Derivatives and Differentiability with
Cylindrical Coordinates . . . . . . . . 11--14
Darrell P. Minor Parrondo's Paradox --- Hope for Losers! 15--20
Russell A. Gordon A Generalization of a Minimum Area
Problem . . . . . . . . . . . . . . . . 21--23
Paul M. Sommers Baseball's All-Stars: Birthplace and
Distribution . . . . . . . . . . . . . . 24--30
Lawrence Brenton and
Thomas G. Edwards Sets of Sets: a Cognitive Obstacle . . . 31--38
Dietrich Trenkler and
Götz Trenkler On the Square Root of $ a a^T + b b^T $ 39--41
W. B. Gearhart and
H. S. Shultz Tugging a Barge with Hyperbolic
Functions . . . . . . . . . . . . . . . 42--49
Anonymous Fallacies, Flaws, and Flimflam . . . . . 50--54
Anonymous Classroom Capsules . . . . . . . . . . . 55--67
Anonymous Problems and Solutions . . . . . . . . . 68--74
Anonymous Media Highlights . . . . . . . . . . . . 75--83
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Yves Nievergelt How (Not) to Solve Quadratic Equations 90--104
Steven Butler Tangent Line Transformations . . . . . . 105--106
Darryl McCullough and
Elizabeth Wade Recursive Enumeration of Pythagorean
Triples . . . . . . . . . . . . . . . . 107--111
Reuben Hersh Independent Thinking . . . . . . . . . . 112--115
Ayoub B. Ayoub The Eccentricity of a Conic Section . . 116--121
Julio Castiñeira Merino Lissajous Figures and Chebyshev
Polynomials . . . . . . . . . . . . . . 122--127
Leonard Lipkin Tossing a Fair Coin . . . . . . . . . . 128--133
Anonymous Fallacies, Flaws, and Flimflam . . . . . 134--138
Anonymous Classroom Capsules . . . . . . . . . . . 139--152
Anonymous Problems and Solutions . . . . . . . . . 153--158
Anonymous Media Highlights . . . . . . . . . . . . 159--167
Anonymous Miscellanea . . . . . . . . . . . . . . 168--172
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Timothy J. Pennings Do Dogs Know Calculus? . . . . . . . . . 178--182
Osvaldo Marrero and
Paul C. Pasles Coin ToGa: a Coin-Tossing Game . . . . . 183--193
M. A. Khan A Class of Exponential Matrices . . . . 194--195
Nial Neger and
Michael Frame Clarifying Compositions with Cobwebs . . 196--204
Panagiotis T. Krasopoulos Tangent Planes of a Quadratic Function 205--206
Jennifer C. Klein and
Thomas Q. Sibley Taking the Sting out of Wasp Nests: a
Dialogue on Modeling in Mathematical
Biology . . . . . . . . . . . . . . . . 207--215
Thomas J. Osler Variations on a Theme from Pascal's
Triangle . . . . . . . . . . . . . . . . 216--223
Anonymous Fallacies, Flaws, and Flimflam . . . . . 224--226
Anonymous Classroom Capsules . . . . . . . . . . . 227--238
Anonymous Problems and Solutions . . . . . . . . . 239--245
Anonymous Media Highlights . . . . . . . . . . . . 246--254
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Greg N. Frederickson A New Wrinkle on an Old Folding Problem 258--263
Susan Jane Colley Calculus, $ \pi $, and the Machine Age 264--269
G. Donald Allen A Survey of Online Mathematics Course
Basics . . . . . . . . . . . . . . . . . 270--279
Hidefumi Katsuura Generalizations of the
Arithmetic--Geometric Mean Inequality
and a Three Dimensional Puzzle . . . . . 280--282
Tevian Dray and
Corinne A. Manogue Using Differentials to Bridge the Vector
Calculus Gap . . . . . . . . . . . . . . 283--290
John F. Putz and
Timothy A. Sipka On Generalizing the Pythagorean Theorem 291--295
Daniel Wilkins The Tangent Lines of a Conic Section . . 296--303
Sharon MacKendrick For What Functions Is $ f^{-1}(x) = 1 /
f(x) $? . . . . . . . . . . . . . . . . 304--311
Anonymous Fallacies, Flaws, and Flimflam . . . . . 312--314
Anonymous Classroom Capsules . . . . . . . . . . . 315--326
Anonymous Problems and Solutions . . . . . . . . . 327--333
Anonymous Media Highlights . . . . . . . . . . . . 334--342
Hardy Grant Book Review . . . . . . . . . . . . . . 343--348
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Michael Dorff and
Leon Hall Solids in $R^n$ Whose Area Is the
Derivative of the Volume . . . . . . . . 350--358
David Perkins A Serendipitous Proof . . . . . . . . . 359--361
David Hecker Constructing a Poincaré Line with
Straightedge and Compass . . . . . . . . 362--366
Jerzy Czyz and
William Self The Rationals Are Countable --- Euclid's
Proof . . . . . . . . . . . . . . . . . 367--369
Janet M. McShane and
Michael I. Ratliff Dice Distributions Using Combinatorics,
Recursion, and Generating Functions . . 370--376
Jack Stewart and
Annalisa Crannell The Band around a (non)Convex Set . . . 377--379
Sharon Barrs and
James Braselton and
Lorraine Braselton A Rational Root Theorem for Imaginary
Roots . . . . . . . . . . . . . . . . . 380--382
Michael J. Bossé and
N. R. Nandakumar When Equalities Are Not Equal: Missing
Mathematical Precision in Teaching,
Texts, and Technology . . . . . . . . . 383--389
Anonymous Fallacies, Flaws, and Flimflam . . . . . 390--393
Anonymous Classroom Capsules . . . . . . . . . . . 394--404
Anonymous Problems and Solutions . . . . . . . . . 405--411
Anonymous Media Highlights . . . . . . . . . . . . 412--420
Anonymous Miscellanea . . . . . . . . . . . . . . 421--422
Frank Swetz Book Review . . . . . . . . . . . . . . 423--423
Anonymous Editorial Board . . . . . . . . . . . . ??
Don Albers In Touch with God: an Interview with
Paul Halmos . . . . . . . . . . . . . . 2--14
Titu Andreescu and
Dorin Andrica On a Diophantine Equation and Its
Ramifications . . . . . . . . . . . . . 15--21
Ranjith Munasinghe Some Linear Differential Equations
Forget That They Have Variable
Coefficients . . . . . . . . . . . . . . 22--25
Brian D. Ginsberg Midy's (Nearly) Secret Theorem --- an
Extension After 165 Years . . . . . . . 26--30
Albert Schueller How Long Was Your Day? . . . . . . . . . 31--33
Harlan J. Brothers Improving the Convergence of Newton's
Series Approximation for $e$ . . . . . . 34--39
Anonymous Fallacies, Flaws, and Flimflam . . . . . 40--42
Anonymous Classroom Capsules . . . . . . . . . . . 43--54
Anonymous Problems and Solutions . . . . . . . . . 55--60
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Lane F. Burgette and
Russell A. Gordon On Determining the Non-Circularity of a
Plane Curve . . . . . . . . . . . . . . 74--83
J. Duncan and
Daniel H. Luecking and
C. M. McGregor On the Values of Pi for Norms on $ R^2 $ 84--92
Gerhard Ströhmer First Order Differential Equations and
the Atmosphere . . . . . . . . . . . . . 93--96
Heba Hathout The Old Hats Problem Revisited . . . . . 97--102
Paul K. Stockmeyer What Did Lincoln Really Mean? . . . . . 103--104
James S. Walker An Elementary Resolution of the Liar
Paradox . . . . . . . . . . . . . . . . 105--111
Reuben Hersh Heron's Area Formula: What About a
Tetrahedron? . . . . . . . . . . . . . . 112--114
N. S. Mendelsohn Tiling with Dominoes . . . . . . . . . . 115--120
Anonymous Fallacies, Flaws, and Flimflam . . . . . 121--124
Anonymous Classroom Capsules . . . . . . . . . . . 125--135
Anonymous Problems and Solutions . . . . . . . . . 136--142
Anonymous Student Research Projects . . . . . . . 143--151
Anonymous Media Highlights . . . . . . . . . . . . 152--160
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J. K. Denny and
C. A. Yackel Temperature Models for Ware Hall . . . . 162--170
James Lesko Sums of Harmonic-Type Series . . . . . . 171--182
Curtis Feist and
Ramin Naimi Almost Alternating Harmonic Series . . . 183--191
Nils P. Johnson The Brachistochrone Problem . . . . . . 192--197
Brian Hopkins and
Robin J. Wilson The Truth about Königsberg . . . . . . . 198--207
Héctor Rosario Simmons' Subliminal Channel . . . . . . 208--212
Anonymous Fallacies, Flaws, and Flimflam . . . . . 213--215
Anonymous Classroom Capsules . . . . . . . . . . . 216--226
Anonymous Problems and Solutions . . . . . . . . . 227--232
Anonymous Media Highlights . . . . . . . . . . . . 233--241
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C. Bryan Dawson and
Troy D. Riggs Highway Relativity . . . . . . . . . . . 246--250
Ioana Mihaila The Rationals of the Cantor Set . . . . 251--255
John E. Morrill Five Mathematicians, a Bunch of
Coconuts, a Monkey, and a Coin . . . . . 256--257
Maurizio Trombetta Tangent Lines and the Inverse Function
Differentiation Rule . . . . . . . . . . 258--261
Daniel Flath and
Cliff Stoll and
Stan Wagon Rocket Math . . . . . . . . . . . . . . 262--273
P. K. Subramanian Successive Differentiation and Leibniz's
Theorem . . . . . . . . . . . . . . . . 274--282
Mark Bailey and
Mike Hilgert and
Herb Bailey Recirculation Models, Homogenized Milk,
and Biotech Applications . . . . . . . . 283--288
Raymond A. Beauregard and
Konstantine D. Zelator On a Three-Dimensional Generalization of
Fermat's Area Theorem . . . . . . . . . 289--291
Wladimir G. Boskoff and
Bogdan D. Suceava When Is Euler's Line Parallel to a Side
of a Triangle? . . . . . . . . . . . . . 292--296
Anonymous Fallacies, Flaws, and Flimflam . . . . . 297--299
Anonymous Classroom Capsules . . . . . . . . . . . 300--309
Anonymous Problems and Solutions . . . . . . . . . 310--317
Anonymous Media Highlights . . . . . . . . . . . . 318--327
Anonymous Editorial Board . . . . . . . . . . . . ??
Michael A. Jones Win, Lose, or Draw: a Markov Chain
Analysis of Overtime in the National
Football League . . . . . . . . . . . . 330--336
Edward W. Packel and
David S. Yuen Projectile Motion with Resistance and
the Lambert $W$ Function . . . . . . . . 337--350
John P. Bonomo and
Carolyn K. Cuff How Do You Stack Up? . . . . . . . . . . 351--361
Stephen M. Walk Mind Your $ \forall $'s and $ \exists
$'s . . . . . . . . . . . . . . . . . . 362--369
Garrett I. Ash and
J. Marshall Ash and
Stefan Catoiu Linearizing Mile Run Times . . . . . . . 370--374
Sudipto Banerjee Revisiting Spherical Trigonometry with
Orthogonal Projectors . . . . . . . . . 375--381
Anonymous Fallacies, Flaws, and Flimflam . . . . . 382--384
Anonymous Classroom Capsules . . . . . . . . . . . 385--401
Anonymous Problems and Solutions . . . . . . . . . 402--408
Anonymous Media Highlights . . . . . . . . . . . . 409--417
Anonymous Editorial Board . . . . . . . . . . . . ??
David E. Zitarelli The Bicentennial of American Mathematics
Journals . . . . . . . . . . . . . . . . 2--15
L. D. Humphreys and
P. J. McKenna Using a Gradient Vector to Find Multiple
Periodic Oscillations in Suspension
Bridge Models . . . . . . . . . . . . . 16--26
Peter R. Mercer Error Estimates For Numerical
Integration Rules . . . . . . . . . . . 27--34
Bryan Dorner Discovering Roots: Ancient, Medieval,
and Serendipitous . . . . . . . . . . . 35--43
Árpád Bényi Finding the Sums of Harmonic Series of
Even Order . . . . . . . . . . . . . . . 44--48
Anonymous Fallacies, Flaws, and Flimflam . . . . . 49--51
Anonymous Classroom Capsules . . . . . . . . . . . 52--72
Anonymous Problems and Solutions . . . . . . . . . 73--79
Anonymous Media Highlights . . . . . . . . . . . . 80--88
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Deanna Haunsperger Saari, with no Apologies . . . . . . . . 90--100
Edward Aboufadel and
Julia Olsen and
Jesse Windle Breaking the Holiday Inn Priority Club
CAPTCHA . . . . . . . . . . . . . . . . 101--108
C. W. Groetsch Another Broken Symmetry . . . . . . . . 109--113
Ezra Brown Phoebe Floats! . . . . . . . . . . . . . 114--122
Clement Falbo The Golden Ratio --- a Contrary
Viewpoint . . . . . . . . . . . . . . . 123--134
Dan Curtis Taking a Whipper-The Fall-Factor Concept
in Rock Climbing . . . . . . . . . . . . 135--140
Anonymous Fallacies, Flaws, and Flimflam . . . . . 141--143
Anonymous Classroom Capsules . . . . . . . . . . . 144--159
Anonymous Problems and Solutions . . . . . . . . . 160--164
Anonymous Media Highlights . . . . . . . . . . . . 165--173
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Don Albers On the Way to ``Mathematical Games'':
Part I of an Interview with Martin
Gardner . . . . . . . . . . . . . . . . 178--190
Harris S. Shultz and
Ray C. Shiflett M&m Sequences . . . . . . . . . . . . . . 191--198
Tian-Xiao He and
Zachariah Sinkala and
Xiaoya Zha If $ F(x) = \int_x^{2 x} f(t) \, d t $
Is Constant, Must $ f(t) = c / t $? . . 199--204
Timothy G. Feeman and
Osvaldo Marrero Intersections of Tangent Lines of
Exponential Functions . . . . . . . . . 205--208
Christopher N. Swanson The Probability an Amazing Card Trick Is
Dull . . . . . . . . . . . . . . . . . . 209--212
Anthony Wexler and
Sherman Stein Making a Bed . . . . . . . . . . . . . . 213--221
Anonymous Fallacies, Flaws, and Flimflam . . . . . 222--223
Anonymous Classroom Capsules . . . . . . . . . . . 224--237
Anonymous Problems and Solutions . . . . . . . . . 238--245
Anonymous Media Highlights . . . . . . . . . . . . 246--254
Keith Devlin Book Review . . . . . . . . . . . . . . 255--256
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Daniel J. Curtin Jan Hudde and the Quotient Rule before
Newton and Leibniz . . . . . . . . . . . 262--272
Jeffrey L. Poet and
Donald L. Vestal, Jr. Curious Consequences of a Miscopied
Quadratic . . . . . . . . . . . . . . . 273--277
Larry Grove The Platonic Solids from their Rotation
Groups . . . . . . . . . . . . . . . . . 278--283
Yung-Pin Chen On Primes, Density Measures, and
Statistical Independence . . . . . . . . 284--288
Mark Bridger and
Andrei Zelevinsky Visibles Revisited . . . . . . . . . . . 289--300
Don Albers ``Mathematical Games'' and Beyond: Part
II of an Interview with Martin Gardner 301--314
Anonymous Fallacies, Flaws, and Flimflam . . . . . 315--317
Anonymous Classroom Capsules . . . . . . . . . . . 318--329
Anonymous Problems and Solutions . . . . . . . . . 330--340
Anonymous Media Highlights . . . . . . . . . . . . 341--349
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Leigh Atkinson When the Pope was a Mathematician . . . 354--362
Poo-Sung Park Ramanujan's Continued Fraction for a
Puzzle . . . . . . . . . . . . . . . . . 363--365
David Richeson Centers of the United States . . . . . . 366--373
Sándor Szabó A Paper-and-Pencil gcd Algorithm for
Gaussian Integers . . . . . . . . . . . 374--380
S. A. Fulling How to Avoid the Inverse Secant (and
Even the Secant Itself) . . . . . . . . 381--387
Philip M. Anselone and
John W. Lee Differentiability of Exponential
Functions . . . . . . . . . . . . . . . 388--393
Anonymous Fallacies, Flaws, and Flimflam . . . . . 394--396
Anonymous Classroom Capsules . . . . . . . . . . . 397--412
Anonymous Problems and Solutions . . . . . . . . . 413--418
Anonymous Media Highlights . . . . . . . . . . . . 419--427
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Dominic Klyve and
Lee Stemkoski Graeco-Latin Squares and a Mistaken
Conjecture of Euler . . . . . . . . . . 2--15
Pierre Perruchet and
Jorge Gallego Do Dogs Know Related Rates Rather than
Optimization? . . . . . . . . . . . . . 16--19
Leonid A. Dickey Do Dogs Know Calculus of Variations? . . 20--23
Thomas J. Osler Archimedes' Quadrature of the Parabola:
a Mechanical View . . . . . . . . . . . 24--28
Walter Meyer David Gaie: Restless Pioneer . . . . . . 29--38
Anonymous Fallacies, Flaws, and Flimflam . . . . . 39--42
Anonymous Classroom Capsules . . . . . . . . . . . 43--53
Anonymous Student Research Projects . . . . . . . 54--58
Anonymous Problems and Solutions . . . . . . . . . 59--68
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Kevin Iga and
Kendra Killpatrick Truck Drivers, a Straw, and Two Glasses
of Water . . . . . . . . . . . . . . . . 82--92
Richard Jerrard and
Joel Schneider and
Ralph Smallberg and
John Wetzel Straw in a Box . . . . . . . . . . . . . 93--102
Gabriela R. Sanchis A Card Trick and the Mathematics Behind
It . . . . . . . . . . . . . . . . . . . 103--109
Raymond A. Beauregard No Arithmetic Cyclic Quadrilaterals . . 110--113
Mark Schlatter How To View A Flatland Painting . . . . 114--120
Anonymous Fallacies, Flaws, and Flimflam . . . . . 121--124
Anonymous Classroom Capsules . . . . . . . . . . . 125--142
Anonymous Problems and Solutions . . . . . . . . . 143--151
Anonymous Media Highlights . . . . . . . . . . . . 152--160
Christopher Hughes Book Review . . . . . . . . . . . . . . 161--164
Anonymous George Pólya Winners . . . . . . . . . . 165--167
Thomas Banchoff Complementary Coffee Cups . . . . . . . 170--175
Leah Wrenn Berman Folding Beauties . . . . . . . . . . . . 176--186
Ying Zhou and
Walter Gall and
Karen Nabb Synchronizing Fireflies . . . . . . . . 187--193
Matthew Boelkins and
Jennifer Miller and
Benjamin Vugteveen From Chebyshev to Bernstein: a Tour of
Polynomials Small and Large . . . . . . 194--204
Donald Francis Young The Tippy Trough . . . . . . . . . . . . 205--213
Anonymous Fallacies, Flaws, and Flimflam . . . . . 214--217
Anonymous Classroom Capsules . . . . . . . . . . . 218--228
Anonymous Problems and Solutions . . . . . . . . . 229--236
Anonymous Media Highlights . . . . . . . . . . . . 237--245
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Dan Kalman The Maximal Deflection on an Ellipse . . 250--260
Daniel J. Teague Group Testing: Four Student Solutions to
a Classic Optimization Problem . . . . . 261--268
J. Aarão and
A. Cox and
C. Jones and
M. Martelli and
A. Westfahl A Non-Smooth Band around a Non-Convex
Region . . . . . . . . . . . . . . . . . 269--278
Duane De Temple and
H. David Reynolds II More Combinatorial Proofs via Flagpole
Arrangements . . . . . . . . . . . . . . 279--285
Michael Z. Spivey Fibonacci Identities via the Determinant
Sum Property . . . . . . . . . . . . . . 286--289
Anonymous Fallacies, Flaws, and Flimflam . . . . . 290--292
Anonymous Classroom Capsules . . . . . . . . . . . 293--307
Anonymous Problems and Solutions . . . . . . . . . 308--318
Anonymous Media Highlights . . . . . . . . . . . . 319--327
Peter Ross Book Review . . . . . . . . . . . . . . 328--331
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Andrew J. Simoson Playing Ball in a Space Station . . . . 334--343
Branko \'Curgus An Exceptional Exponential Function . . 344--354
O-Yeat Chan and
James Smoak More Designer Decimals: The Integers and
Their Geometric Extensions . . . . . . . 355--363
Carl V. Lutzer and
James E. Marengo The Divergence of Balanced Harmonic-like
Series . . . . . . . . . . . . . . . . . 364--369
Scott H. Brown An Interview with H. W. Gould . . . . . 370--379
Anonymous Fallacies, Flaws, and Flimflam . . . . . 380--384
Anonymous Classroom Capsules . . . . . . . . . . . 385--391
Anonymous Problems and Solutions . . . . . . . . . 392--397
Anonymous Media Highlights . . . . . . . . . . . . 398--408
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Don Albers John Todd --- Numerical Mathematics
Pioneer . . . . . . . . . . . . . . . . 2--23
Tanya Leise As the Planimeter's Wheel Turns:
Planimeter Proofs for Calculus Class . . 24--31
Michael W. Ecker Maximizing the Probability of a Big
Sweepstakes Win . . . . . . . . . . . . 32--36
Brian Albright An Introduction to Simulated Annealing 37--42
Anonymous Fallacies, Flaws, and Flimflam . . . . . 43--46
Anonymous Problems and Solutions . . . . . . . . . 60--67
Anonymous Media Highlights . . . . . . . . . . . . 68--76
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David Alan Brooks A New Method of Trisection . . . . . . . 78--81
Donald L. Muench An Iterative Angle Trisection . . . . . 82--84
Adrian Rice and
Eve Torrence ``Shutting up like a telescope'': Lewis
Carroll's ``Curious'' Condensation
Method for Evaluating Determinants . . . 85--95
Murray Schechter Which Way Is Jerusalem? Navigating on a
Spheroid . . . . . . . . . . . . . . . . 96--105
Walter Meyer The Origins of Finite Mathematics: The
Social Science Connection . . . . . . . 106--118
Wai Yan Pong Sums of Consecutive Integers . . . . . . 119--123
Allen D. Rogers Integrals of Fitted Polynomials and an
Application to Simpson's Rule . . . . . 124--130
Anonymous Fallacies, Flaws, and Flimflam . . . . . 131--134
Anonymous Classroom Capsules . . . . . . . . . . . 135--147
Anonymous Problems and Solutions . . . . . . . . . 148--156
Anonymous Media Highlights . . . . . . . . . . . . 157--164
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Donald Teets The Mathematics of ``Go To'' Telescopes 170--178
Leith Hathout Not Just Hats Anymore: Binomial
Inversion and the Problem of Multiple
Coincidences . . . . . . . . . . . . . . 179--184
Laura A. Zager and
George C. Verghese Caps and Robbers: What Can You Expect? 185--191
Michael Frame and
Nial Neger Newton's Method and the Wada Property: a
Graphical Approach . . . . . . . . . . . 192--204
Thomas P. Dence Some Half-Row Sums from Pascal's
Triangle via Laplace Transforms . . . . 205--209
Richard Hammack A Geometric View of Complex
Trigonometric Functions . . . . . . . . 210--217
Anonymous Fallacies, Flaws, and Flimflam . . . . . 218--220
Anonymous Classroom Capsules . . . . . . . . . . . 221--226
Anonymous Problems and Solutions . . . . . . . . . 227--232
Anonymous Media Highlights . . . . . . . . . . . . 233--240
Martin Gardner Book Review . . . . . . . . . . . . . . 241--242
Anonymous Editorial Board . . . . . . . . . . . . ??
Edward Rozema Epidemic Models for SARS and Measles . . 246--259
Alex Fink and
Richard Guy The Number-Pad Game . . . . . . . . . . 260--264
Khristo N. Boyadzhiev Equiangular Surfaces, Self-Similar
Surfaces, and the Geometry of Seashells 265--271
Manjinder S. Bains and
J. B. Thoo The Normals to a Parabola and the Real
Roots of a Cubic . . . . . . . . . . . . 272--277
Thomas J. Osler and
Abdulkadir Hassen and
Tirupathi R. Chandrupatla Surprising Connections between
Partitions and Divisors . . . . . . . . 278--287
Byungchul Cha Transcendental Functions and Initial
Value Problems: a Different Approach to
Calculus II . . . . . . . . . . . . . . 288--296
Anonymous Fallacies, Flaws, and Flimflam . . . . . 297--299
Anonymous Classroom Capsules . . . . . . . . . . . 300--303
Anonymous Student Research Projects . . . . . . . 304--308
Anonymous Problems and Solutions . . . . . . . . . 309--318
Anonymous Media Highlights . . . . . . . . . . . . 319--327
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Andrew J. Simoson Pursuit Curves for the Man in the Moone 330--338
Paul K. Stockmeyer More Mathematics in the Bedroom: a
Paradoxical Probability . . . . . . . . 339--344
Richard Parris Commensurable Triangles . . . . . . . . 345--355
Roland Minton and
Timothy J. Pennings Do Dogs Know Bifurcations? . . . . . . . 356--361
C. A. Yackel and
J. K. Denny Partial Fractions in Calculus, Number
Theory, and Algebra . . . . . . . . . . 362--374
Anonymous Fallacies, Flaws, and Flimflam . . . . . 375--377
Anonymous Classroom Capsules . . . . . . . . . . . 378--387
Anonymous Problems and Solutions . . . . . . . . . 388--396
Anonymous Media Highlights . . . . . . . . . . . . 397--404
Gerald L. Alexanderson Book Review . . . . . . . . . . . . . . 405--408
Anonymous Referees in 2006 . . . . . . . . . . . . 409--410
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John Bukowski Christiaan Huygens and the Problem of
the Hanging Chain . . . . . . . . . . . 2--11
Richard Hess and
Charles Grinstead and
Marshall Grinstead and
Deborah Bergstrand Hermit Points on a Box . . . . . . . . . 12--23
William Dickinson and
Mohammad Salmassi \em The Right \em Right Triangle on the
Sphere . . . . . . . . . . . . . . . . . 24--33
Paul Loomis and
Michael Plytage and
John Polhill Summing Up the Euler $ \phi $ Function 34--42
C. W. Groetsch The Depletion Ratio . . . . . . . . . . 43--48
Anonymous Fallacies, Flaws, and Flimflam . . . . . 49--50
Anonymous Classroom Capsules . . . . . . . . . . . 51--64
Anonymous Problems and Solutions . . . . . . . . . 65--73
Anonymous Media Highlights . . . . . . . . . . . . 74--82
Anonymous George Pólya Awards . . . . . . . . . . . 83--86
Anonymous Editorial Board . . . . . . . . . . . . ??
Richard P. Jerrard and
John E. Wetzel Universal Stoppers Are Rupert . . . . . 90--94
Thomas J. Bannon and
Robert E. Bradley Mind the Gap . . . . . . . . . . . . . . 95--101
Alexander Karabegov and
Jason Holland Finding All Solutions to the Magic
Hexagram . . . . . . . . . . . . . . . . 102--106
Jane Arledge and
Sarah Tekansik A New Property of Repeating Decimals . . 107--111
Ezra Brown and
Jason C. Brunson Fibonacci's Forgotten Number . . . . . . 112--120
William R. Vautaw Two Problems with Table Saws . . . . . . 121--128
Lawrence Brenton Remainder Wheels and Group Theory . . . 129--135
Anonymous Fallacies, Flaws, and Flimflam . . . . . 136--138
Anonymous Classroom Capsules . . . . . . . . . . . 139--152
Anonymous Problems and Solutions . . . . . . . . . 153--161
Anonymous Media Highlights . . . . . . . . . . . . 162--170
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Deanna Haunsperger A Break for Mathematics: an Interview
with Joe Gallian . . . . . . . . . . . . 174--190
Arthur T. Benjamin and
Jennifer J. Quinn An Alternate Approach to Alternating
Sums: a Method to DIE for . . . . . . . 191--202
Jack Douthett and
Richard J. Krantz Dinner Tables and Concentric Circles: a
Harmony of Mathematics, Music, and
Physics . . . . . . . . . . . . . . . . 203--211
Russell A. Gordon Squaring a Circular Segment . . . . . . 212--220
William F. Edwards and
Ray C. Shiflett and
Harris S. Shultz Dependent Probability Spaces . . . . . . 221--226
Anonymous Fallacies, Flaws, and Flimflam . . . . . 227--229
Anonymous Classroom Capsules . . . . . . . . . . . 230--239
Anonymous Problems and Solutions . . . . . . . . . 240--247
Anonymous Media Highlights . . . . . . . . . . . . 248--256
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Greg N. Frederickson Designing a Table Both Swinging and
Stable . . . . . . . . . . . . . . . . . 258--266
Dimitri Dziabenko and
Oleg Ivrii Centaurs: Here, There, Everywhere! . . . 267--272
Travis Kowalski How to Measure Angles with a Ruler . . . 273--279
Kevin Iga The Truck Driver's Straw Problem and
Cantor Sets . . . . . . . . . . . . . . 280--290
Tom Farmer A Helical Stairway Project . . . . . . . 291--298
Anonymous Fallacies, Flaws, and Flimflam . . . . . 299--300
Anonymous Classroom Capsules . . . . . . . . . . . 301--306
Anonymous Problems and Solutions . . . . . . . . . 307--314
Anonymous Media Highlights . . . . . . . . . . . . 315--323
Gregory S. Goodhart Review . . . . . . . . . . . . . . . . . 324--326
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Andrew Rich Leftist Numbers . . . . . . . . . . . . 330--336
Clifton Cunningham Report from the Ambassador to Cida-2 . . 337--345
John P. Bonomo \em You Can \em Teach an Old Magician
New Tricks . . . . . . . . . . . . . . . 346--356
Greg Martin Sets That Contain Their Circle Centers 357--366
Leon Harkleroad Tuning with Triangles . . . . . . . . . 367--373
Stelios Kapranidis and
Reginald Koo Variations of the Sliding Ladder Problem 374--379
Anonymous Fallacies, Flaws, and Flimflam . . . . . 380--386
Anonymous Classroom Capsules . . . . . . . . . . . 387--400
Anonymous Problems and Solutions . . . . . . . . . 401--409
Anonymous Media Highlights . . . . . . . . . . . . 410--418
Gerald L. Alexanderson Review . . . . . . . . . . . . . . . . . 419--421
Anonymous George PóLya Awards . . . . . . . . . . . 422--424
Anonymous Referees in 2007 . . . . . . . . . . . . 425--427
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Andy Liu Two Applications of a Hamming Code . . . 2--5
Henry F. Ahner Sledge-Hammer Integration . . . . . . . 6--9
Michael Sheard Trick or Technique? . . . . . . . . . . 10--14
Vaughan Pratt Factoring Heron . . . . . . . . . . . . 15--16
Raymond A. Beauregard Diametric Quadrilaterals with Two Equal
Sides . . . . . . . . . . . . . . . . . 17--21
Andrew J. Simoson Solomon's Sea and $ \pi $ . . . . . . . 22--32
Andrew T. Barker Evolutionary Stability in the Traveler's
Dilemma . . . . . . . . . . . . . . . . 33--38
Hasan Unal Proof Without Words: Sum of an Infinite
Series . . . . . . . . . . . . . . . . . 39--39
Anonymous Classroom Capsules . . . . . . . . . . . 40--46
Warren Page Introduction . . . . . . . . . . . . . . 47--54
Anonymous Problems and Solutions . . . . . . . . . 55--64
Cecil Rousseau Book Reviews . . . . . . . . . . . . . . 65--67
Anonymous Media Highlights . . . . . . . . . . . . 68--76
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Greg Oman An Independent Axiom System for the Real
Numbers . . . . . . . . . . . . . . . . 78--86
Alan Sultan CORDIC: How Hand Calculators Calculate 87--92
Curtis Feist and
Ramin Naimi Topology Explains Why Automobile
Sunshades Fold Oddly . . . . . . . . . . 93--98
Thomas Koshy Lobb's Generalization of Catalan's
Parenthesization Problem . . . . . . . . 99--107
Anderson Norton Eighty-eight Thousand, Four Hundred and
Eighteen (More) Ways to Fill Space . . . 108--112
Ulrich A. Hoensch A ``Paperclip'' Approach to Curvature,
Torsion, and the Frénet--Serret Formulas 113--118
Anonymous Student Research Projects . . . . . . . 119--124
Anonymous Classroom Capsules . . . . . . . . . . . 125--130
Anonymous Problems and Solutions . . . . . . . . . 131--141
Reuben Hersh Book Reviews . . . . . . . . . . . . . . 142--145
Anonymous Media Highlights . . . . . . . . . . . . 146--155
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Anonymous Interview with Martin Gardner . . . . . 158--161
Martin Gardner $L$-Tromino Tiling of Mutilated
Chessboards . . . . . . . . . . . . . . 162--168
Stewart Coffin Polyomino Problems to Confuse Computers 169--173
Ryan M. Pedersen and
Timothy L. Vis Sets of Mutually Orthogonal Sudoku Latin
Squares . . . . . . . . . . . . . . . . 174--181
Herb Bailey Jeeps Penetrating a Hostile Desert . . . 182--187
Caleb Emmons Three Poems . . . . . . . . . . . . . . 188--188
Marc Zucker Flipping Triangles! . . . . . . . . . . 189--195
Hang Chen and
Curtis Cooper $n$-Card Tricks . . . . . . . . . . . . 196--203
R. Douglas Chatham Reflections on the $ N + k $ Queens
Problem . . . . . . . . . . . . . . . . 204--210
M. Oskar van Deventer Puzzling Mechanisms, Part 4: Tricky
Triplet . . . . . . . . . . . . . . . . 211--211
Gary Kennedy and
Stephen Kennedy Crossword Puzzle: $ \pi_1 \approx Z
\oplus Z $ . . . . . . . . . . . . . . . 212--212
Anonymous Classroom Capsules . . . . . . . . . . . 213--214
Anonymous Problems and Solutions . . . . . . . . . 215--221
Susan Jane Colley and
Mark Bollman Book Reviews . . . . . . . . . . . . . . 222--225
Anonymous Solutions to Puzzles and Brainteasers 226--227
Anonymous Media Highlights . . . . . . . . . . . . 228--236
Anonymous Editorial Board . . . . . . . . . . . . ??
Barry Cox and
Stan Wagon Mechanical Circle-Squaring . . . . . . . 238--247
Richard Maruszewski Fibonacci's Forgotten Number Revisited 248--251
Árpád Bényi and
loan Casu Pompeiu's Theorem Revisited . . . . . . 252--258
Hongwei Chen The Fresnel Integrals Revisited . . . . 259--262
Andrew J. Simoson Maximizing the Spectacle of Water
Fountains . . . . . . . . . . . . . . . 263--274
Hidefumi Katsuura Summations Involving Binomial
Coefficients . . . . . . . . . . . . . . 275--278
Eugene C. Boman False Position, Double False Position
and Cramer's Rule . . . . . . . . . . . 279--283
Anonymous Classroom Capsules . . . . . . . . . . . 284--292
Anonymous Problems and Solutions . . . . . . . . . 293--305
Margaret A. M. Murray and
Reuben Hersh Reviews . . . . . . . . . . . . . . . . 306--312
Anonymous Media Highlights . . . . . . . . . . . . 313--320
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Robert D. Poodiack and
Kevin J. LeClair Fundamental Theorems of Algebra for the
Perplexes . . . . . . . . . . . . . . . 322--336
James Graham-Eagle The Draining Cylinder . . . . . . . . . 337--344
Mike Krebs and
Caleb Emmons and
Anthony Shaheen How to Differentiate an Integer Modulo
$n$ . . . . . . . . . . . . . . . . . . 345--353
Jer-Chin (Luke) Chuang Minimal Solutions to the Box Problem . . 354--360
Jiu Ding and
Zizhong Wang Dynamics of Exponential Functions . . . 361--369
Robert A. Fontenot Correlation of the Union of Two
Bivariate Data Sets . . . . . . . . . . 370--373
Lior Bary-Soroker and
Eli Leher On the Remainder in the Taylor Theorem 373--375
Anonymous Problems and Solutions . . . . . . . . . 376--383
Deborah Bacharach Book Review . . . . . . . . . . . . . . 384--386
Anonymous Media Highlights . . . . . . . . . . . . 387--396
Anonymous Referees in 2008 . . . . . . . . . . . . 397--398
Anonymous Additions, Corrections, Emendations, and
Revisions . . . . . . . . . . . . . . . 399--399
Anonymous Editorial Board . . . . . . . . . . . . ??
Reuben Hersh Under-represented Then Over-represented:
a Memoir of Jews in American Mathematics 2--9
Michael Bolt and
Daniel C. Isaksen Dogs Don't Need Calculus . . . . . . . . 10--16
John Martin The Helen of Geometry . . . . . . . . . 17--28
Michael Naylor and
Brian Winkel Biangular Coordinates Redux: Discovering
a New Kind of Geometry . . . . . . . . . 29--41
Manuel Lopez and
James Marengo An Upper Bound for the Expected Range of
a Random Sample . . . . . . . . . . . . 42--48
Rick Mabry The Hardest Straight-In Pool Shot . . . 49--57
Jim Hartman Computing Definite Inegrals using the
Definition . . . . . . . . . . . . . . . 58--60
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Mother of Modern Algebra, by M. B. W.
Tent . . . . . . . . . . . . . . . . . . 72--73
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Friendship: What a Teacher and a Student
Learned about Life While Corresponding
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Elizabeth Arnold and
Stephen Lucas and
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Dan Curtis What's My Domain? . . . . . . . . . . . 113--121
David Seppala-Holtzman The Dance of the Foci . . . . . . . . . 122--128
Anurag Agarwal and
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Joseph B. Dence and
Thomas P. Dence Four Ways to Skin a Definite Integral 134--144
Jaime Cruz-Sampedro and
Margarita Tetlalmatzi-Montiel POEM's and Newton's Aerodynamic Frustum 145--153
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Frank Wang Application of the Lambert $W$ Function
to the SIR Epidemic Model . . . . . . . 156--159
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Frank Morgan Fermat's Last Theorem for Fractional and
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Rick Kreminski Taylor's Theorem: The Elusive $c$ is Not
So Elusive . . . . . . . . . . . . . . . 186--192
John E. Wetzel When Are Two Figures Congruent? . . . . 193--196
Michael Z. Spivey Deranged Exams . . . . . . . . . . . . . 197--202
Elias Abboud Viviani's Theorem and Its Extension . . 203--211
Conway Xu A Characterization of a Quadratic
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Duane W. DeTemple Counting Squares to Sum Squares . . . . 214--221
Kent E. Morrison The FedEx Problem . . . . . . . . . . . 222--232
Nicole Yunger Halpern Three Poems . . . . . . . . . . . . . . 233--234
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Julius Barbanel A Geometric Approach to Fair Division 268--280
Theodore P. Hill and
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Brian Hopkins Taking Turns . . . . . . . . . . . . . . 289--297
Angela Vierling-Claassen Who Does the Housework? . . . . . . . . 298--302
Thomas C. Ratliff Lewis Carroll, Voting, and the Taxicab
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Michael Rothenberg The Tower and Glass Marbles Problem . . 350--356
Michael N. Fried and
Mayer Goldberg A Pumping Lemma for Invalid Reductions
of Fractions . . . . . . . . . . . . . . 357--364
Shiv K. Gupta and
Waclaw Szymanski Cubic Polynomials with Rational Roots
and Critical Points . . . . . . . . . . 365--369
Claudi Alsina and
Roger B. Nelsen Proof Without Words: New
Pythagorean-like Theorems . . . . . . . 370--370
Dave Boyles Finding Rational Parametric Curves of
Relative Degree One or Two . . . . . . . 371--382
Jody Sorensen and
Elyn Rykken Sprinkler Bifurcations and Stability . . 383--391
Hasan Unal Proof Without Words: Double Sum for Sine
and Cosine . . . . . . . . . . . . . . . 392--392
Alif Anggoro and
Eddy Liu and
Angus Tulloch The Rascal Triangle . . . . . . . . . . 393--395
M. Axtell and
J. Stickles Graphs and Zero-Divisors . . . . . . . . 396--399
Bettina Richmond On a Perplexing Polynomial Puzzle . . . 400--403
Yixun Shi Sum-Difference Numbers . . . . . . . . . 404--405
Eric F. Mazzone and
Bruce R. Piper Animating Nested Taylor Polynomials to
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Anonymous Problems and Solutions . . . . . . . . . 409--415
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Leslie A. Cheteyan and
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Michael A. Jones Chutes and Ladders for the Impatient . . 2--8
Reginald Koo and
Martin Jones Probability 1/e . . . . . . . . . . . . 9--13
Anonymous Anne Burns Explains How \em Iterated
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David Swanson The Band Around a Convex Body . . . . . 15--24
Julius B. Barbanel and
Steven J. Brams Two-Person Pie-Cutting: The Fairest Cuts 25--32
Charlotte Simmons Augustus De Morgan Behind the Scenes . . 33--40
Jesse Byrne Teaching Tip: Actuarial Science and
Gompertz's Law of Mortality . . . . . . 40--42
Deanna Leggett and
John Perry and
Eve Torrence Computing Determinants by
Double-Crossing . . . . . . . . . . . . 43--54
Vagarshak Vardanyan Teaching Tip: Correcting Cramer's Rule 54--55
Ursula Whitcher Boundary Conditions . . . . . . . . . . 56--56
Jack E. Graver An Elementary Treatment of General Inner
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Ben Mathes and
Chris Dow and
Leo Livshits Cantor Groups . . . . . . . . . . . . . 60--61
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Mohammad Torabi Dashti Faulhaber's Triangle . . . . . . . . . . 96--97
P. K. Aravind How Spherical Are the Archimedean Solids
and Their Duals? . . . . . . . . . . . . 98--107
Nikolai Krylov and
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Robert K. Smither The Symmedian Point: Constructed and
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Richard Parris Lattice Cubes . . . . . . . . . . . . . 118--125
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Karl-Dieter Crisman The Symmetry Group of the Permutahedron 135--139
Michael A. Jones Mathematical Minute: Removing a Dot . . 139--139
Anne Fontaine and
Susan Hurley Golden Matrix Families . . . . . . . . . 140--147
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Kenneth Schilling Book Review: \booktitleLogical
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Bonnie Gold How Your Philosophy of Mathematics
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Andrew J. Simoson Newton's Radii, Maupertuis' Arc Length,
and Voltaire's Giant . . . . . . . . . . 183--190
T. S. Michael Guards, Galleries, Fortresses, and the
Octoplex . . . . . . . . . . . . . . . . 191--200
Joseph Gani and
Randall Swift Random Breakage of a Rod into Unit
Lengths . . . . . . . . . . . . . . . . 201--205
R. A. Beauregard Teaching Tip: a Slippery Slope . . . . . 206--206
Diego Dominici An Arithmetic Metric . . . . . . . . . . 207--214
Meg B. Huddleston Teaching Tip: Practice Integration on
Problem Triplets . . . . . . . . . . . . 214--214
Joseph Petrillo Counting Subgroups in a Direct Product
of Finite Cyclic Groups . . . . . . . . 215--222
Michele Intermont and
Aileen Murphy An Application of Group Theory to Change
Ringing . . . . . . . . . . . . . . . . 223--228
Dan Hathaway Using Continuity Induction . . . . . . . 229--231
Anonymous Problems and Solutions . . . . . . . . . 232--240
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Stephen M. Walk The Intermediate Value Theorem Is NOT
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to You . . . . . . . . . . . . . . . . . 254--259
Dominic Klyve and
Anna Lauren An Empirical Approach to the St.
Petersburg Paradox . . . . . . . . . . . 260--264
Greg N. Frederickson Folding Polyominoes from One Level to
Two . . . . . . . . . . . . . . . . . . 265--274
Dan Joseph and
Gregory Hartman and
Caleb Gibson Generalized Parabolas . . . . . . . . . 275--282
Sergei Ovchinnikov Series with Inverse Function Terms . . . 283--288
Andrew Jobbings From the Dance of the Foci to a
Strophoid . . . . . . . . . . . . . . . 289--298
Mark Schwartz Do Dogs Know the Trammel of Archimedes? 299--308
Annalisa Crannell The Shad--Fack Transom . . . . . . . . . 309--316
Jack E. Graver Making Change Efficiently . . . . . . . 317--322
Roger Eggleton and
Vladimir Kustov The Product and Quotient Rules Revisited 323--326
John Mason A Generalization of the Parabolic Chord
Property . . . . . . . . . . . . . . . . 326--328
Anonymous Problems and Solutions . . . . . . . . . 329--335
Kent E. Morrison Book Review . . . . . . . . . . . . . . 336--338
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Geoffrey Birky and
Connie Campbell and
Manya Raman and
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Bruce Torrence The Easiest Lights Out Games . . . . . . 361--372
Andy Liu Is Parallelism an Equivalence Relation? 372--372
Ken Luther Teaching Tip: Is This Integral Zero? . . 373--373
Eszter K. Horváth and
Attila Máder and
Andreja Tepavcevi\'c One-dimensional Czédli-type Islands . . . 374--378
Jeffrey Clark Derivative Sign Patterns . . . . . . . . 379--382
Michael W. Ecker Limit Interchange and L'Hôpital's Rule 382--383
Herb Bailey and
Dan Kalman Walking with a Slower Friend . . . . . . 384--387
Thomas E. Goebeler, Jr. The Cobb--Douglas Function and Hölder's
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Juan D. Serna and
Amitabh Joshi The Center of Mass of a Soft Spring . . 389--394
Keith J. Coates An Intuitive Proof of the Singular Value
Decomposition of a Matrix . . . . . . . 394--396
Carlos F. Borges Discretization vs. Rounding Error in
Euler's Method . . . . . . . . . . . . . 396--399
William R. Green Abel's Theorem Simplifies Reduction of
Order . . . . . . . . . . . . . . . . . 399--402
Thomas J. Pfaff Averaging Sums of Powers of Integers . . 402--404
B. Sury Uncountably Generated Ideals of
Functions . . . . . . . . . . . . . . . 404--406
Anonymous Problems and Solutions . . . . . . . . . 407--412
Samuel Goldberg Book Review . . . . . . . . . . . . . . 413--415
Anonymous Media Highlights . . . . . . . . . . . . 416--425
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Martin Gardner Hexaflexagons . . . . . . . . . . . . . 2--5
Ionut E. Iacob and
T. Bruce McLean and
Hua Wang The V-flex, Triangle Orientation, and
Catalan Numbers in Hexaflexagons . . . . 6--10
Les Pook From Hexaflexagons to Edge Flexagons to
Point Flexagons . . . . . . . . . . . . 11--14
Ian Stewart Cups and Downs . . . . . . . . . . . . . 15--19
Tanya Khovanova Martin Gardner's Mistake . . . . . . . . 20--24
Robert Bekes and
Jean Pedersen and
Bin Shao Mad Tea Party Cyclic Partitions . . . . 25--36
John Watkins Triangular Numbers, Gaussian Integers,
and KenKen . . . . . . . . . . . . . . . 37--42
David Applegate and
Marc LeBrun and
N. J. A. Sloane Carryless Arithmetic Mod 10 . . . . . . 43--50
Greg N. Frederickson Bracing Regular Polygons As We Race into
the Future . . . . . . . . . . . . . . . 51--57
Arthur T. Benjamin Squaring, Cubing, and Cube Rooting . . . 58--64
Karl Schaffer A Platonic Sextet for Strings . . . . . 64--69
Gary Kennedy and
Stephen Kennedy The Play's the Thing! . . . . . . . . . 70--71
John D. Beasley Magic Knight's Tours . . . . . . . . . . 72--75
Darren Glass The Secretary Problem from the
Applicant's Point of View . . . . . . . 76--81
sarah-marie belcastro The Continuing Saga of Snarks . . . . . 82--87
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Ronald E. Mickens An Exactly Solvable Model for the Spread
of Disease . . . . . . . . . . . . . . . 114--121
Colin Foster Teaching Tip: How to Manipulate Test
Scores . . . . . . . . . . . . . . . . . 121--122
Matthew Glomski and
Edward Ohanian Eradicating a Disease: Lessons from
Mathematical Epidemiology . . . . . . . 123--132
Ezra Halleck Teaching Tip: Consider a Circular Cow 133--133
Brian Hopkins 30 Years of Bulgarian Solitaire . . . . 135--140
Thomas Koshy and
Zhenguang Gao Convergence of a Catalan Series . . . . 141--146
Yossi Elran Retrolife and The Pawns Neighbors . . . 147--151
Jorge Moraleda and
David G. Stork Lake Wobegon Dice . . . . . . . . . . . 152--159
Aviezri S. Fraenkel Ratwyt . . . . . . . . . . . . . . . . . 160--164
Paul Martin and
Kirthi Premadasa The Optimal Level of Insulation in a
Home Attic . . . . . . . . . . . . . . . 165--168
Keith E. Mellinger and
Raymond Viglione The Spider and the Fly . . . . . . . . . 169--172
Suk-Geun Hwang A Real Proof of the Principal Axis
Theorem . . . . . . . . . . . . . . . . 172--173
Anonymous Problems and Solutions . . . . . . . . . 174--180
David A. Cox Book Review . . . . . . . . . . . . . . 181--183
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Michael Augros Rediscovering Pascal's Mystic Hexagon 194--202
Jacob A. Siehler The Finite Lamplighter Groups: a Guided
Tour . . . . . . . . . . . . . . . . . . 203--211
Michael A. Jones Proof Without Words: The Square of a
Balancing Number Is a Triangular Number 212--212
Timothy Kohl When Abelian = Hausdorff . . . . . . . . 213--215
Javier Sánchez-Reyes The Catenary as Roulette . . . . . . . . 216--219
Carl Swenson and
André Yandl Partitioning Pythagorean Triangles Using
Pythagorean Angles . . . . . . . . . . . 220--225
Claudi Alsina and
Roger B. Nelsen Proof Without Words: The Pythagorean
Theorem with Equilateral Triangles . . . 226--226
Donald Teets Push-To Telescope Mathematics . . . . . 227--231
Brian Albright The Distribution of the Sum of Signed
Ranks . . . . . . . . . . . . . . . . . 232--236
Hongwei Chen and
Chris Kennedy Harmonic Series Meets Fibonacci Sequence 237--243
David Benko The Basel Problem as a Telescoping
Series . . . . . . . . . . . . . . . . . 244--250
Andrew M. Ross Designing Medical Tests: The Other Side
of Bayes' Theorem . . . . . . . . . . . 251--254
Michael Deveau and
Robie Hennigar Quotient-Rule-Integration-by-Parts . . . 254--256
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John Dodge and
Andrew Simoson Ben-Hur Staircase Climbs . . . . . . . . 274--284
Javier Sánchez-Reyes The Hyperbolic Sine Cardinal and the
Catenary . . . . . . . . . . . . . . . . 285--290
Li Zhou Teaching Tip: When does $ f(g(x)) = x $? 290--290
Óscar Ciaurri and
Emilio Fernández and
Rodolfo Larrea and
Luz Roncal Vi\`ete's Product Proved in the Finest
Ancient Style . . . . . . . . . . . . . 291--296
Joe DeMaio Counting Triangles to Sum Squares . . . 297--303
Theodore Rice Teaching Tip: Are You Changing the
Rules? Again? . . . . . . . . . . . . . 304--304
Ioannis M. Roussos On the Steiner Minimizing Point and the
Corresponding Algebraic System . . . . . 305--308
Li Zhou Viviani Polytopes and Fermat Points . . 309--312
Brian S. Thomson A Strong Kind of Riemann Integrability 313--321
Anthony J. Crachiola Proof Without Words: Partial Sums of an
Arithmetic Sequence . . . . . . . . . . 321--321
Reuben Hersh Why the Faulhaber Polynomials Are Sums
of Even or Odd Powers of $ (n + 1 / 2) $ 322--324
Hidefumi Katsuura Extending the Alternating Series Test 325--330
Robert Kantrowitz and
Michael Schramm Series that Converge Absolutely but
Don't Converge . . . . . . . . . . . . . 331--333
Vadim Ponomarenko and
Natalie Selinski Two Semigroup Elements Can Commute with
Any Positive Rational Probability . . . 334--336
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Timothy W. Jones Euler's Identity, Leibniz Tables, and
the Irrationality of Pi . . . . . . . . 361--364
Joe Latulippe and
Jennifer Switkes Sometimes \em Newton's Method Always \em
Cycles . . . . . . . . . . . . . . . . . 365--370
Roger B. Nelsen Proof Without Words: an Alternating
Series . . . . . . . . . . . . . . . . . 370--370
Götz Trenkler and
Dietrich Trenkler The Numerical Range of the Luoshu Is a
Piece of Cake --- Almost . . . . . . . . 371--376
Xingya Fan and
Yixin Zhu Proof Without Words: The Sine Is
Subadditive on $ [0, \pi] $ . . . . . . 376--376
Satyanand Singh A Fifth Way to Skin a Definite Integral 377--378
David Betounes Better Than Optimal By Taking A Limit? 379--386
William Derrick and
James Hirstein Proof Without Words: Ptolemy's Theorem 386--386
David Seppala-Holtzman An Optimal Basketball Free Throw . . . . 387--394
Tom Brown and
Brian Pasko Winning a Racquetball Match . . . . . . 395--400
Thomas Q. Sibley Idempotents \`a la mod . . . . . . . . . 401--404
J. K. Denny Rational exponentials and continued
fractions . . . . . . . . . . . . . . . 405--407
Paul Yiu Geometry of sum-difference numbers . . . 408--409
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Marcio Diniz Asset Pricing, Financial Markets, and
Linear Algebra . . . . . . . . . . . . . 2--8
Nat Kell and
Matt Kretchmar Suspense at the Ballot Box . . . . . . . 9--16
Madeubek Kungozhin and
Sidney Kung Proof Without Words: an Algebraic
Inequality . . . . . . . . . . . . . . . 16--16
Tevian Dray Using Differentials to Differentiate
Trigonometric and Exponential Functions 17--23
Valerii Faiziev and
Robert Powers and
Prasanna Sahoo When Can One Expect a Stronger Triangle
Inequality? . . . . . . . . . . . . . . 24--31
Mike Krebs and
Natalie Martinez The Combinatorial Trace Method in Action 32--36
Geoff Goehle and
Mitsuo Kobayashi Polynomial Graphs and Symmetry . . . . . 37--42
Dong Fengming and
Ho Weng Kin and
Lee Tuo Yeong A Family of Identities via Arbitrary
Polynomials . . . . . . . . . . . . . . 43--47
Yukio Kobayashi Proof Without Words: Tangent Double
Angle Identity . . . . . . . . . . . . . 47--47
Avner Halevy Old Tails and New Trails in High
Dimensions . . . . . . . . . . . . . . . 48--52
Micha\l Misiurewicz Irrational Square Roots . . . . . . . . 53--55
Kurt Fink and
Jawad Sadek Other Indeterminate Forms . . . . . . . 55--57
Neal Brand and
John A. Quintanilla Modeling Terminal Velocity . . . . . . . 57--61
Richard Olson Book Review: \booktitleThe Lost
Millennium: History's Timetables under
Siege (2nd edition), by Florin Diacu . . 62--63
Samuel Goldberg Book Review: \booktitleProbability Tales
by Charles M. Grinstead, William P.
Peterson, and J. Laurie Snell . . . . . 64--64
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Betty Mayfield Women and Mathematics in the Time of
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Adam E. Parker Who Solved the Bernoulli Differential
Equation and How Did They Do It? . . . . 89--97
William J. Cook An $n$-dimensional Pythagorean Theorem 98--101
Kenneth Schilling Derivative Sign Patterns in Two
Dimensions . . . . . . . . . . . . . . . 102--108
J. Ding and
N. H. Rhee Teaching Tip: When a Matrix and Its
Inverse Are Stochastic . . . . . . . . . 108--109
Paul Isihara and
Doeke Buursma Multi-Peg Tower of Hanoi . . . . . . . . 110--116
L. R. King An Ellipse Morphs to a Cosine Graph! . . 117--123
Daniel Bravo and
Joseph Fera Mathematical Minute: Rotating a Function
Graph . . . . . . . . . . . . . . . . . 124--125
Ryan Hoban Euclidean, Spherical, and Hyperbolic
Shadows . . . . . . . . . . . . . . . . 126--134
Purna Patel and
Raymond Viglione Proof Without Words: a Variation on
Thébault's First Problem . . . . . . . . 135--135
Herb Bailey Slouching in the Rain . . . . . . . . . 136--138
Hongwei Chen A New Ratio Test for Positive Monotone
Series . . . . . . . . . . . . . . . . . 139--141
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J. K. Denny SAGE: Open Source Mathematics Software
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Peter Zizler Quiz Today: Should I Skip Class? . . . . 166--170
Joe DeMaio Proof Without Words: an Alternating Sum
of Squares . . . . . . . . . . . . . . . 170--170
David Benko and
John Molokach The Basel Problem as a Rearrangement of
Series . . . . . . . . . . . . . . . . . 171--176
Paul Bruckman and
Joseph B. Dence and
Thomas P. Dence and
Justin Young Series of Reciprocal Triangular Numbers 177--184
Gordon A. Swain Archimedes Curves . . . . . . . . . . . 185--189
Yukio Kobayashi Proof without Words: Triangular Sums . . 189--189
Jeremiah William Johnson The Number of Group Homomorphisms from $
D_m $ into $ D_n $ . . . . . . . . . . . 190--192
James Sandefur and
John Mason Circular Inclusion . . . . . . . . . . . 193--201
Ryan Stuffelbeam How Weird Are Weird Fractions? . . . . . 202--209
Anurag Agarwal and
James E. Marengo and
Likin C. Simon Romero System Lifetimes, The Memoryless
Property, Euler's Constant, and $ \pi $ 210--219
David James and
Cynthia Botteron Understanding Singular Vectors . . . . . 220--226
Fuchang Gao A Simple Proof of the Right-Hand Rule 227--229
Walden Freedman Sharing the Work . . . . . . . . . . . . 229--232
Anonymous Problems and Solutions . . . . . . . . . 233--240
Robert E. Bradley Book Review: \booktitleJourney through
Mathematics: Creative Episodes in Its
History by Enrique A. González-Velasco 241--243
Susan Jane Colley Book Review: \booktitleThe Manga Guide
to Linear Algebra, by Shin Takahashi,
illustrated by Iroha Inoue and
\booktitleMath Girls, by Hiroshi Yuki
(translated by Tony Gonzalez) . . . . . 244--247
Anonymous Media Highlights . . . . . . . . . . . . 248--255
Anonymous Editorial Board . . . . . . . . . . . . ??
Mark Baker and
Jane Beltran and
Jason Buell and
Brian Conrey and
Tom Davis and
Brianna Donaldson and
Jeanne Detorre-Ozeki and
Leila Dibble and
Tom Freeman and
Robert Hammie and
Julie Montgomery and
Avery Pickford and
Justine Wong Sets, Planets, and Comets . . . . . . . 258--264
Tom Richmond and
Aaron Young Instant Insanity II . . . . . . . . . . 265--272
L. Taalman and
A. Tongen and
B. Warren and
F. Wyrick-Flax and
I. Yoon Mancala Matrices . . . . . . . . . . . . 273--283
Roger B. Nelsen Proof Without Words: Squares Modulo 3 283--283
Andrew MacLaughlin and
Alex Meadows Chomp in Disguise . . . . . . . . . . . 284--292
Jonathan Needleman Boggle Logic Puzzles: Minimal Solutions 293--299
Oscar Levin and
Gerri M. Roberts Counting Knights and Knaves . . . . . . 300--306
Joe DeMaio and
Hong Lien Tran Domination and Independence on a
Triangular Honeycomb Chessboard . . . . 307--314
Frank Bermudez and
Anthony Medina and
Amber Rosin and
Eren Scott Are Stupid Dice Necessary? . . . . . . . 315--322
Marc Chamberland Proof Without Words: The Area of an
Inner Square . . . . . . . . . . . . . . 322--322
Colin Day A Power Rule Proof without Limits . . . 323--324
Anonymous Problems and Solutions . . . . . . . . . 325--331
Gizem Karaali Book Review . . . . . . . . . . . . . . 332--335
Anonymous Media Highlights . . . . . . . . . . . . 336--344
Anonymous Editorial Board . . . . . . . . . . . . ??
Mary Lou Zeeman Mathematics, Sustainability, and a
Bridge to Decision Support . . . . . . . 346--349
Jim Walsh and
Richard McGehee Modeling Climate Dynamically . . . . . . 350--363
Charles R. Hadlock Underground Mathematics . . . . . . . . 364--375
Meredith L. Greer and
Holly A. Ewing and
Kathryn L. Cottingham and
Kathleen C. Weathers Collaborative Understanding of
Cyanobacteria in Lake Ecosystems . . . . 376--385
Osvaldo Marrero Seasonal Variation in Epidemiology . . . 386--398
Christiane Rousseau How Inge Lehmann Discovered the Inner
Core of the Earth . . . . . . . . . . . 399--408
Xiaoxue H. Li Proof Without Words: Monotonicity of $
\sin x / x $ on $ (0, \pi / 2) $ . . . . 408--408
Gregory Mark Boudreaux and
Jess E. Walls Descartes' Calculus of Subnormals: What
Might Have Been . . . . . . . . . . . . 409--420
Xiaoxue H. Li Proof Without Words: Monotonicity of $
\tan x / x $ on $ (0, \pi / 2) $ . . . . 420--420
John Zobitz Forest Carbon Uptake and the Fundamental
Theorem of Calculus . . . . . . . . . . 421--424
Emek Köse and
Jennifer Kunze Climate Modeling in the Calculus and
Differential Equations Classroom . . . . 424--427
Lily Khadjavi About the Pace of Climate Change: Write
a Report to the President . . . . . . . 428--432
Erik R. Tou A Typology for Finite Groups . . . . . . 432--436
Anonymous Problems and Solutions . . . . . . . . . 437--445
Ben Fusaro Book Review and Commentary . . . . . . . 446--449
Anonymous Media Highlights . . . . . . . . . . . . 450--456
Anonymous Referees In 2013 . . . . . . . . . . . . 457--458
Anonymous Additions, Corrections, Emendations, and
Revisions . . . . . . . . . . . . . . . 458--460
Anonymous Editorial Board . . . . . . . . . . . . ??
Brian Hopkins From the Editor: Constancy and Change 2--2
John P. Bonomo Not All Numbers Can Be Created Equally 3--10
Horia I. Petrache Correspondence Between Geometric and
Differential Definitions of the Sine and
Cosine . . . . . . . . . . . . . . . . . 11--15
Roger Nelsen Proof Without Words: Alternating Sums of
Consecutive Squares . . . . . . . . . . 16--16
Yonah Cherniavsky and
Artour Mouftakhov Zbikowski's Divisibility Criterion . . . 17--21
Munir Mahmood and
Ibtihal Mahmood Proof Without Words: Completing the
Square via the Difference of Squares . . 21--21
Sam Vandervelde An Acute Case of Discontinuity . . . . . 22--28
Ádám Besenyei Traveling Waves and Taylor Series: Do
They Have Something in Common? . . . . . 29--32
Louis Bohorquez and
Jennifer Switkes American Roulette: a Gambler's Ruin . . 33--40
Vincent J. Matsko Second-Order Recurrences with
Nonconsecutive Initial Conditions . . . 41--49
David Seppala-Holtzman Proof Without Words: Ensphering Three
Capped Prisms . . . . . . . . . . . . . 49--49
Ruth I. Berger Green Jello World and Escher's World . . 50--53
Ollie Nanyes Continuously Differentiable Curves
Detect Limits of Functions of Two
Variables . . . . . . . . . . . . . . . 54--56
Anonymous Problems and Solutions . . . . . . . . . 57--64
Anonymous Film Review . . . . . . . . . . . . . . 65--70
Anonymous Media Highlights . . . . . . . . . . . . 71--78
Anonymous George Pólya Awards for 2013 . . . . . . 79--79
Anonymous Editorial Board . . . . . . . . . . . . ??
Brian Hopkins From the Editor: Anonymity and Youth . . 82--82
Fiacha Heneghan and
Kyle Petersen Power Series for Up-Down Min-Max
Permutations . . . . . . . . . . . . . . 83--91
Arthur T. Benjamin and
Ethan J. Brown Challenging Magic Squares for Magicians 92--100
Michael Bolt and
Anthony Meyer and
Nicholas Visser The Fastest Way Not to Run a Four-Minute
Mile . . . . . . . . . . . . . . . . . . 101--107
Nick Loehr Classifying Nilpotent Maps via Partition
Diagrams . . . . . . . . . . . . . . . . 108--115
Yukio Kobayashi Proof Without Words: Componendo et
Dividendo, a Theorem on Proportions . . 115--115
Elizabeth Field and
Rachael Ivison and
Amanda Reyher and
Steven Warner Truck Versus Human: Mathematics Under
Pressure . . . . . . . . . . . . . . . . 116--120
Steven Edwards Proof Without Words: an Infinite Series
Using Golden Triangles . . . . . . . . . 120--120
Jeremy LeCrone and
Nancy Ann Neudauer Matroids on Groups? . . . . . . . . . . 121--128
Leigh Marie Braswell and
Tanya Khovanova Cookie Monster Devours Naccis . . . . . 129--135
Claudi Alsina and
Roger Nelsen and
Hasan Unal Proof Without Words: The Difference of
Consecutive Integer Cubes Is Congruent
to 1 Modulo 6 . . . . . . . . . . . . . 135--135
Michelle Soule A Single Family of Semigroups with Every
Positive Rational Commuting Probability 136--139
Daniel McQuillan and
Rob Poodiack On the Differentiation Formulae for
Sine, Tangent, and Inverse Tangent . . . 140--142
Connie Xu A Proof for a Quadratic Function without
Using Calculus . . . . . . . . . . . . . 143--144
Anonymous Problems and Solutions . . . . . . . . . 145--151
Anonymous Media Highlights . . . . . . . . . . . . 152--159
Anonymous Editorial Board . . . . . . . . . . . . ??
Michael Brilleslyper and
Beth Schaubroeck Locating Unimodular Roots . . . . . . . 162--168
Meighan Dillon Projective Geometry for All . . . . . . 169--178
Roger Nelsen Proof Without Words: Pythagorean
Quadruples . . . . . . . . . . . . . . . 179--179
Vincent Coll and
Jeremy Davis and
Martin Hall and
Colton Magnant and
James Stankewicz and
Hua Wang Integer Solutions to Box Optimization
Problems . . . . . . . . . . . . . . . . 180--190
Long Wang Proof Without Words: Sine Sum Identity 190--190
Karl-Dieter Crisman and
Mike Veatch Reinventing Heron . . . . . . . . . . . 191--197
Guanshen Ren Proof Without Words: Pythagoras for a
Right Trapezoid . . . . . . . . . . . . 198--198
Daniel T. Clancy and
Steven J. Kifowit A Closer Look at Bobo's Sequence . . . . 199--206
Christopher Lee and
Valerie Peterson The Rank of Recurrence Matrices . . . . 207--215
Guanshen Ren Proof Without Words: Pythagoras for a
Clipped Rectangle . . . . . . . . . . . 216--216
O. A. S. Karamzadeh Johnson's Three Circles Theorem
Revisited . . . . . . . . . . . . . . . 217--218
Jorge Martín-Morales and
Antonio M. Oller-Marcén Computing Volumes of Solids of
Revolution with Double Integrals . . . . 219--221
Anonymous Problems and Solutions . . . . . . . . . 222--229
Tanya Khovanova Book Review . . . . . . . . . . . . . . 230--231
Anonymous Media Highlights . . . . . . . . . . . . 232--239
Anonymous Editorial Board . . . . . . . . . . . . ??
Tomas Rokicki Towards God's Number for Rubik's Cube in
the Quarter-Turn Metric . . . . . . . . 242--253
Calvin Armstrong and
Susan Goldstine Exhibit Review . . . . . . . . . . . . . 254--256
David Joyner The Man Who Found God's Number . . . . . 258--266
Michael A. Jones and
Brittany C. Shelton and
Miriam E. Weaverdyck On God's Number(s) for Rubik's Slide . . 267--275
Charlie Smith Math Frenzy . . . . . . . . . . . . . . 276--277
Stan Wagon Graph Theory Problems from Hexagonal and
Traditional Chess . . . . . . . . . . . 278--287
Paul Salomon Imbalance Puzzles . . . . . . . . . . . 288--288
Darcie Connors and
Darren Glass Chutes and Ladders with Large Spinners 289--295
Oscar Levin Story Puzzles . . . . . . . . . . . . . 296--296
Jason Rosenhouse Knights, Knaves, Normals, and Neutrals 297--306
David Nacin Permudoku Puzzle . . . . . . . . . . . . 307--307
Michael Henle Book Review . . . . . . . . . . . . . . 308--312
Charles L. Cooper and
Michael S. McClendon A Topological Definition of Limits for
Use in Elementary Calculus . . . . . . . 313--315
Stephan Berendonk Stretched Circles are Conic Sections, A
Geometric Proof . . . . . . . . . . . . 316--317
Anonymous Problems And Solutions . . . . . . . . . 318--323
Anonymous Media Highlights . . . . . . . . . . . . 324--331
Anonymous Crossword Puzzle Solution . . . . . . . 332--333
Anonymous Editorial Board . . . . . . . . . . . . ??
Jeff Suzuki The Self-Limiting Partisan Gerrymander:
an Optimization Approach . . . . . . . . 338--348
Roger B. Nelsen Proof Without Words: Summing Squares by
Counting Triangles . . . . . . . . . . . 349--349
Whitney Rhianna Fillers and
Bill Linderman and
Andrew Simoson Mancala as Nim . . . . . . . . . . . . . 350--356
Hasan Unal Proof Without Words: an Arctangent
Identity . . . . . . . . . . . . . . . . 357--357
Lisa Rougetet A Prehistory of Nim . . . . . . . . . . 358--363
Ángel Plaza Proof Without Words: Limit of a
Recursive Arithmetic Mean . . . . . . . 364--364
Brian K. Miceli A Combinatorial Proof of a Theorem of
Katsuura . . . . . . . . . . . . . . . . 365--369
Long Wang Proof Without Words: Cosine Difference
Identity . . . . . . . . . . . . . . . . 370--370
Asya Shpiro Unfamiliar Properties of Familiar Shapes 371--375
Roger B. Nelsen Proof Without Words: a Sine Identity for
Triangles . . . . . . . . . . . . . . . 376--376
Kimberly Leung and
Chris Rasmussen and
Samuel S. P. Shen and
Dov Zazkis Calculus from a Statistics Perspective 377--386
Hasan Unal Proof Without Words: a Formula of
Hermann . . . . . . . . . . . . . . . . 387--387
Marc Frantz Hyperbola: Under Construction! . . . . . 388--390
Branko \'Curgus A Squeeze for Two Common Sequences That
Converge to $e$ . . . . . . . . . . . . 391--392
Anonymous Problems and Solutions . . . . . . . . . 393--399
Brian Hopkins Book Review . . . . . . . . . . . . . . 400--405
Anonymous Media Highlights . . . . . . . . . . . . 406--413
Anonymous George Pólya Awards for 2014 . . . . . . 414--415
Anonymous Referees in 2014 . . . . . . . . . . . . 415--416
Anonymous Editorial Board . . . . . . . . . . . . ??
Brian Hopkins From the Editor: Celebration and Delay 2--2
Michael A. Jones and
Jennifer Wilson Adjusting Child Support Payments in
Michigan . . . . . . . . . . . . . . . . 3--9
Roger B. Nelsen Proof Without Words: The Area of a
Regular Dodecagon . . . . . . . . . . . 10--10
Sherman Stein What Distributes Over Exponentiation? 11--14
Lucio Cadeddu and
Giampaolo Lai Maxima and Minima Without Derivatives? 15--22
David Richeson Proof Without Words: The Maximum Sum of
Inradii . . . . . . . . . . . . . . . . 23--23
Michael Maltenfort Secants, Tangents, Rotations, and
Reflections . . . . . . . . . . . . . . 24--34
Daniel Acosta and
Terry Lawson Weak Contractions and Fixed Points . . . 35--41
Roger B. Nelsen Proof Without Words: a Trigonometric
Proof of the Arithmetic Mean--Geometric
Mean Inequality . . . . . . . . . . . . 42--42
Thomas Bannon The Origin of Quaternions . . . . . . . 43--50
Nam Gu Heo Proof Without Words: The Pythagorean
Theorem . . . . . . . . . . . . . . . . 51--51
Zsolt Lengvárszky Proving the Pythagorean Theorem by
Letting the Sides Vary . . . . . . . . . 52--55
David Lowry-Duda Unexpected Conjectures about $ - 5 $
Modulo Primes . . . . . . . . . . . . . 56--57
Richard Bedient and
Courtney Gibbons Grandma Makes Granola . . . . . . . . . 58--60
Anonymous Problems and Solutions . . . . . . . . . 61--66
Dominic Klyve Book Review . . . . . . . . . . . . . . 67--72
Anonymous Media Highlights . . . . . . . . . . . . 73--80
Anonymous Editorial Board . . . . . . . . . . . . ??
Steve J. Bacinski and
Mark J. Panaggio and
Timothy J. Pennings Elvis Lives: Mathematical Surprises
Inspired by Elvis, the Welsh Corgi . . . 82--91
Kathleen Bell and
Shania Polson and
Tom Richmond The Fastest Path Between Two Points,
with a Symmetric Obstacle . . . . . . . 92--97
Roger B. Nelsen Proof Without Words: Sums of Every Third
Triangular Number . . . . . . . . . . . 98--98
Nicholas Cotton and
Cam McLeman and
Daniel Pinchock On Combining and Convolving Fractals . . 99--108
Matthew Jakubowski and
Raymond Viglione Proof Without Words: The Vertex Angle
Sum of a Regular Star Polygon . . . . . 109--109
Dae S. Hong When Is the Generating Function of the
Fibonacci Numbers an Integer? . . . . . 110--112
Ricardo Alfaro Sequences of Power Lines . . . . . . . . 113--120
K. B. Subramaniam Proof Without Words: Cotangent Double
Angle Identity . . . . . . . . . . . . . 121--121
Julia E. Bergner and
Christopher D. Walker Groupoid Cardinality and Egyptian
Fractions . . . . . . . . . . . . . . . 122--129
Gunhan Caglayan Proof Without Words: Series of
Reciprocals of Tetrahedral Numbers . . . 130--130
Edward Early and
Patrick Kim and
Michael Proulx Goldbach's Pigeonhole . . . . . . . . . 131--135
Cristinel Mortici A Very Elementary Proof of Bernoulli's
Inequality . . . . . . . . . . . . . . . 136--137
Ulrich Abel On an Identity Involving Powers of
Binomial Coefficients . . . . . . . . . 138--138
Robert Kantrowitz and
Michael Neumann Another Face of the Archimedean Property 139--141
Anonymous Problems and Solutions . . . . . . . . . 142--148
Jiang-Ping Jeff Chen Book Review . . . . . . . . . . . . . . 149--152
Anonymous Media Highlights . . . . . . . . . . . . 153--160
Anonymous Editorial Board . . . . . . . . . . . . ??
David Richeson Circular Reasoning: Who First Proved
That $C$ Divided by $d$ Is a Constant? 162--171
Roger B. Nelsen Proof Without Words: Each But Two
Triangular Numbers Is a Sum of Three
Triangular Numbers . . . . . . . . . . . 172--172
Eleanor Farrington Parametric Equations at the Circus:
Trochoids and Poi Flowers . . . . . . . 173--177
Michael H. Peters On the Shrinking Volume of the
Hypersphere . . . . . . . . . . . . . . 178--180
Juan D. Serna Partial Proof Without Words: Shaping
Some Cases of the Erd\Hos--Straus
Conjecture . . . . . . . . . . . . . . . 181--181
Robert L. Foote and
Xidian Sun An Intrinsic Formula for the Cross Ratio
in Spherical and Hyperbolic Geometries 182--188
Dave Boyles Rational and Implicit Equations for Some
Polar Curves . . . . . . . . . . . . . . 189--196
Hassan Boualem and
Robert Brouzet To Be (a Circle) or Not to Be? . . . . . 197--206
Adam Glesser and
James Shade and
Bogdan D. Suceava On the Inverse Curvature Problem . . . . 207--214
Eric Thurschwell An Even Simpler Proof of the Right-Hand
Rule . . . . . . . . . . . . . . . . . . 215--217
Haryono Tandra An Inductive Proof of the Compactness of
the Closed Unit Ball of an Arbitrary
Dimension . . . . . . . . . . . . . . . 218--219
Anonymous Problems and Solutions . . . . . . . . . 220--227
Christina C. Garrett Book Review . . . . . . . . . . . . . . 228--232
Anonymous Media Highlights . . . . . . . . . . . . 233--240
Anonymous Editorial Board . . . . . . . . . . . . ??
Richard E. Chatwin and
Dana Mackenzie How to Win at (One-Round) War . . . . . 242--253
David Nacin MAA 100th Anniversary CMJ Puzzle A . . . 254--254
Dana Rowland Candy Crush Combinatorics . . . . . . . 255--262
David Nacin MAA 100th Anniversary CMJ Puzzle C . . . 263--263
Gordon Hamilton and
Kiran S. Kedlaya and
Henri Picciotto Square-Sum Pair Partitions . . . . . . . 264--269
Brian J. Birgen The Uniqueness of
Rock--Paper--Scissors--Lizard--Spock . . 270--273
David Nacin MAA 100th Anniversary CMJ Puzzle J . . . 274--274
Jathan Austin and
Susanna Molitoris-Miller The Settlers of Catan: Using Settlement
Placement Strategies in the Probability
Classroom . . . . . . . . . . . . . . . 275--282
Tanya Khovanova and
Joshua Xiong Cookie Monster Plays Games . . . . . . . 283--293
David Nacin MAA 100th Anniversary CMJ Puzzle M . . . 294--294
Robert W. Vallin A Magic Trick Leads to an Identity: Some
Induction Fun . . . . . . . . . . . . . 295--298
Denis Bell Area of a Circle via the Second
Fundamental Theorem of Calculus . . . . 299--299
Anonymous Problems and Solutions . . . . . . . . . 300--308
Joseph O'Rourke Book Review . . . . . . . . . . . . . . 309--314
Anonymous Media Highlights . . . . . . . . . . . . 315--322
Anonymous MAA 100th Anniversary CMJ Puzzles
Solutions . . . . . . . . . . . . . . . 323--323
Anonymous Editorial Board . . . . . . . . . . . . ??
Ezra Brown Saints and Scoundrels and Two Theorems
That Are Really the Same . . . . . . . . 326--334
Roger B. Nelsen Proof Without Words: Centered Triangular
Numbers . . . . . . . . . . . . . . . . 335--335
Brian D. Beasley and
David R. Stone Journal Problems Sections: Modern
Challenges and Teaching Tools . . . . . 336--346
Meiyue Shao Proof Without Words: Bounding the
Euler--Mascheroni Constant . . . . . . . 347--347
Cosmin Pohoata and
Richard Stong A Sufficient Condition for Subgroups
with Prime Indices to Be Normal . . . . 348--351
Elizabeth Knapper and
Hope McIlwain Predicting Wins and Losses: a Volleyball
Case Study . . . . . . . . . . . . . . . 352--358
José Luis Cereceda Explicit Form of the Faulhaber
Polynomials . . . . . . . . . . . . . . 359--363
Kambiz Razminia A Short Proof of Symmetric Inequalities 364--366
Zengxiang Tong A Note on the Fundamental Theorem of
Calculus . . . . . . . . . . . . . . . . 367--368
Anonymous Problems and Solutions . . . . . . . . . 369--376
Anonymous Book Review: \booktitleExcerpts from MAA
Interviews . . . . . . . . . . . . . . . 377--384
Anonymous Media Highlights . . . . . . . . . . . . 385--392
Anonymous George Pólya Awards for 2015 . . . . . . 393--394
Anonymous Notes on Volume 45 . . . . . . . . . . . 395--397
Anonymous Referees in 2015 . . . . . . . . . . . . 398--399
Anonymous Editorial Board . . . . . . . . . . . . ??
Jacqueline Leake and
Nicholas Pritchard The Advantage of the Coin Toss for the
New Overtime System in the National
Football League . . . . . . . . . . . . 2--9
Roger B. Nelsen Proof Without Words: The
Pentagon--Hexagon--Decagon Identity . . 10--10
Brian Bradie Yet More Ways to Skin a Definite
Integral . . . . . . . . . . . . . . . . 11--18
Allan Berele and
Stefan Catoiu Area and Perimeter Bisecting Lines of a
Triangle . . . . . . . . . . . . . . . . 19--28
Greg Oman and
Victoria Slattum A Characterization of the Cyclic Groups
by Subgroup Indices . . . . . . . . . . 29--33
Paul T. Allen Boundary Value Problems and Finite
Differences . . . . . . . . . . . . . . 34--41
Andrew Leahy William Neile's Contribution to Calculus 42--49
Leonard Littleton and
Russell May Simplified Expectations in the Birthday
Problem . . . . . . . . . . . . . . . . 50--55
Heiko Hoffmann Weighted AM-GM Inequality via Elementary
Multivariable Calculus . . . . . . . . . 56--58
Ricardo E. Rojas Waiter! One Classic Calculus Problem,
Hold the Calculus . . . . . . . . . . . 59--60
Anonymous Problems and Solutions . . . . . . . . . 61--66
Anne Quinn Technology Review: Graph Theory
Smartphone Apps . . . . . . . . . . . . 67--72
Anonymous Media Highlights . . . . . . . . . . . . 73--80
Anonymous Editorial Board . . . . . . . . . . . . ??
Fred Kuczmarski Rubber Band Calculus . . . . . . . . . . 82--93
Roger B. Nelsen Proof Without Words: a Surprising
Integer Result . . . . . . . . . . . . . 94--94
Viktor Blåsjö How to Find the Logarithm of Any Number
Using Nothing But a Piece of String . . 95--100
Colin Foster Proof Without Words: Integer Right
Triangle Hypotenuses Without Pythagoras 101--101
William Kronholm Integration by the Wrong Parts . . . . . 102--105
Michael Maltenfort A Canine Conundrum, or What Would Elvis
Do? . . . . . . . . . . . . . . . . . . 106--107
Roger B. Nelsen Proof Without Words: The Golden Ratio 108--108
Glenn Ledder Empirical Modeling: Choosing Models and
Fitting Them to Data . . . . . . . . . . 109--119
C. David Leach Proof Without Words: Powers of Three and
Triangular Numbers . . . . . . . . . . . 120--120
Marc Zucker Lattice Paths and Harmonic Means . . . . 121--124
Ángel Plaza Proof Without Words: Arithmetic Mean of
Two Means . . . . . . . . . . . . . . . 125--125
Howard Sporn Abbott-and-Costello Numbers . . . . . . 126--132
Paisley Rekdal Philip Larkin's Koan . . . . . . . . . . 133--133
Samuel G. Moreno A Short and Elementary Proof of the
Basel Problem . . . . . . . . . . . . . 134--135
C. W. Groetsch De Morgan's Series Test . . . . . . . . 136--137
Anonymous Problems and Solutions . . . . . . . . . 138--145
Peter Ross Book Review . . . . . . . . . . . . . . 146--152
Anonymous Media Highlights . . . . . . . . . . . . 153--160
Anonymous Editorial Board . . . . . . . . . . . . ??
Robert L. Foote and
Han Nie How to Approximate the Volume of a Lake 162--170
Roger B. Nelsen Proof Without Words: Perfect Numbers and
Triangular Numbers . . . . . . . . . . . 171--171
Xianglong Ni Iterating the Logarithmic Function . . . 172--178
Roger B. Nelsen Proof Without Words: Square Triangular
Numbers and Almost Isosceles Pythagorean
Triples . . . . . . . . . . . . . . . . 179--179
Amy Nesky and
Clara Redwood Discrete and Smooth Bicycle ``Unicycle''
Paths . . . . . . . . . . . . . . . . . 180--189
Roger B. Nelsen Proof Without Words: Nearly Cubic
Pythagorean Boxes . . . . . . . . . . . 190--190
Adam E. Parker What's in a Name: Why Cauchy and Euler
Share the Cauchy--Euler Equation . . . . 191--198
John Molokach Proof Without Words: The Product-to-Sum
Identities . . . . . . . . . . . . . . . 199--199
Todd Abel and
Jeremy Brazas Pedagogically Inconvenient Functions for
Teaching Transformations . . . . . . . . 200--206
Tom Edgar Proof Without Words: Matchstick
Triangles . . . . . . . . . . . . . . . 207--207
Mahesh Agarwal and
Narasimhamurthi Natarajan Inheritance Relations of Hexagons and
Ellipses . . . . . . . . . . . . . . . . 208--214
Neil Aitken Babbage and Carroll in the Silent
Workshop, 1867 . . . . . . . . . . . . . 215--215
Amal Sharif-Rasslan A Visual Approach to Geometric Series
with Negative Ratio . . . . . . . . . . 216--218
Michael Spivey The Chu--Vandermonde Identity via
Leibniz's Identity for Derivatives . . . 219--220
Anonymous Problems and Solutions . . . . . . . . . 221--227
Heidi Burgiel Book Review . . . . . . . . . . . . . . 228--231
Anonymous Media Highlights . . . . . . . . . . . . 232--239
Anonymous Editorial Board . . . . . . . . . . . . ??
Michael A. Jones and
Alexander Webb and
Jennifer Wilson Rankings over Time . . . . . . . . . . . 242--248
David Nacin MAA 101st Anniversary CMJ Puzzle A . . . 249--249
Kathleen Ryan and
Brittany Shelton Statistics on the Bonus Round of Wheel
of Fortune . . . . . . . . . . . . . . . 250--253
David Nacin MAA 101st Anniversary CMJ Puzzle C . . . 254--254
M. A. Diniz and
D. Lopes and
A. Polpo and
L. E. B. Salasar The Sticker Collector's Problem . . . . 255--263
David Nacin MAA 101st Anniversary CMJ Puzzle J . . . 264--264
Timothy E. Goldberg Algebra From Geometry in the Card Game
SET . . . . . . . . . . . . . . . . . . 265--273
David Nacin MAA 101st Anniversary CMJ Puzzle M . . . 274--274
Joel Pasternack and
Stewart Venit Horse Racing Odds: Can You Beat the
Track by Hedging Your Bets? . . . . . . 275--281
Arthur Benjamin and
Rohan Chandra Multiplying by 9 . . . . . . . . . . . . 281--281
Patrick Sullivan The FA Cup Draw and Pairing Up
Probabilities . . . . . . . . . . . . . 282--292
David Nacin MAA 101st Anniversary CMJ Puzzles
Solutions . . . . . . . . . . . . . . . 293--293
Stephen Scheinberg The Generalized Birthday Problem . . . . 294--296
John Engbers and
Adam Hammett A Direct Proof of the Integral Formulae
for the Inverse Hyperbolic Functions . . 297--299
Anonymous Problems and Solutions . . . . . . . . . 300--306
Raymond N. Greenwell Book Review . . . . . . . . . . . . . . 307--311
Anonymous Media Highlights . . . . . . . . . . . . 312--319
Anonymous Editorial Board . . . . . . . . . . . . ??
Travis Kowalski The Sine of a Single Degree . . . . . . 322--332
Sarah Blake Form . . . . . . . . . . . . . . . . . . 333--333
Melissa Mark and
Michael Schramm When You Wander off on a Tangent, Where
Do You End Up? . . . . . . . . . . . . . 334--339
sarah-marie belcastro and
Tamara Veenstra Do the Twist! (on Polygon-Base Boxes) 340--345
Miyeon Kwon Proof Without Words: The Lateral Surface
Area of a Conical Frustum . . . . . . . 346--346
John P. Bonomo Winning a Pool Is Harder Than You
Thought . . . . . . . . . . . . . . . . 347--355
Roger B. Nelsen Proof Without Words: a Right Triangle
Identity . . . . . . . . . . . . . . . . 355--355
Kaushik Basu A New and Rather Long Proof of the
Pythagorean Theorem by Way of a
Proposition on Isosceles Triangles . . . 356--360
Franz Lemmermeyer Leonardo da Vinci's Proof of the
Pythagorean Theorem . . . . . . . . . . 361--364
Piotr Josevich Trigonometric Derivatives Made Easy . . 365--366
Armen Bagdasaryan and
Josep Batle Algebraic Characterization of Two
Independent Events . . . . . . . . . . . 367--368
Anonymous Problems and Solutions . . . . . . . . . 369--374
Brian Hopkins Book Review . . . . . . . . . . . . . . 375--380
Jennifer Wilson Film Review . . . . . . . . . . . . . . 381--385
Anonymous Media Highlights . . . . . . . . . . . . 386--393
Anonymous George Pólya Awards for 2016 . . . . . . 394--395
Anonymous Notes on Volume 46 . . . . . . . . . . . 396--397
Anonymous Referees in 2016 . . . . . . . . . . . . 398--399
Anonymous Editorial Board . . . . . . . . . . . . ??
James Grime The Bizarre World of Nontransitive Dice:
Games for Two or More Players . . . . . 2--9
Alex Schaefer and
Jay Schweig Balanced Nontransitive Dice . . . . . . 10--16
Roger B. Nelsen Proof Without Words: Perfect Numbers
Modulo 7 . . . . . . . . . . . . . . . . 17--17
Ben Blum-Smith and
Samuel Coskey The Fundamental Theorem on Symmetric
Polynomials: History's First Whiff of
Galois Theory . . . . . . . . . . . . . 18--29
Jordie Albiston A Plane Angle Poem . . . . . . . . . . . 30--30
Julie Millett and
Xingping Sun Existence of Limits and Continuity . . . 31--35
García Capitán Francisco Javier Proof Without Words: Tangents of 15 and
75 Degrees . . . . . . . . . . . . . . . 35--35
Sandy Ganzell Divisibility Tests, Old and New . . . . 36--40
Óscar Ciaurri Proof Without Words: an
Arithmetic--Geometric Series . . . . . . 41--41
Michael A. Carchidi and
Robert L. Higgins Covariances Between Transient States in
Finite Absorbing Markov Chains . . . . . 42--50
Ángel Plaza Proof Without Words: The Triangle with
Maximum Area for a Given Base and
Perimeter . . . . . . . . . . . . . . . 51--51
John Beam A Powerful Method of Non-Proof . . . . . 52--54
Michael Maltenfort A Function Worth a Second Look . . . . . 55--57
Anonymous Problems and Solutions . . . . . . . . . 58--63
Jenna P. Carpenter Book Review . . . . . . . . . . . . . . 64--68
Craig S. Kaplan Book Review . . . . . . . . . . . . . . 69--72
Anonymous Media Highlights . . . . . . . . . . . . 73--80
Anonymous Editorial Board . . . . . . . . . . . . ??
Antonella Perucca The Chinese Remainder Clock . . . . . . 82--89
Tom Edgar and
N. Chris Meyer A Visual Validation of Vi\`ete's
Verification . . . . . . . . . . . . . . 90--96
Prapanpong Pongsriiam Integral Values of the Generating
Functions of Fibonacci and Lucas Numbers 97--101
Donald Teets Computing a Satellite Orbit From
Photographs . . . . . . . . . . . . . . 102--110
Kazim Ali Forgotten Equations . . . . . . . . . . 111--111
Edward R. Forringer Pythagorean Triples for Easy Solutions
of Certain Quadratics and a Newly
Generated Tree . . . . . . . . . . . . . 112--114
Howard Sporn Pythagorean Triples, Complex Numbers,
and Perplex Numbers . . . . . . . . . . 115--122
Steven J. Miller and
Cesar E. Silva If a Prime Divides a Product \ldots . . 123--128
Mircea Merca On the Arithmetic Mean of the Square
Roots of the First $n$ Positive Integers 129--133
Francisco Javier García Capitán Homographic Pencils for the Ellipse and
the Hyperbola . . . . . . . . . . . . . 134--136
Bennett Eisenberg A Very Short Proof that the Sum of
Independent Normal Random Variables Is
Normal . . . . . . . . . . . . . . . . . 137--137
Anonymous Problems and Solutions . . . . . . . . . 138--145
Thomas Dick Book Review . . . . . . . . . . . . . . 146--152
Anonymous Media Highlights . . . . . . . . . . . . 153--160
Anonymous Editorial Board . . . . . . . . . . . . ??
Stephen Kaczkowski Mathematical Models for Global Mean Sea
Level Rise . . . . . . . . . . . . . . . 162--169
Donald Illich Water Mathematics . . . . . . . . . . . 170--170
Stuart M. Anderson and
Owen D. Byer Finding Polygonal Areas with the Corset
Theorem . . . . . . . . . . . . . . . . 171--178
Eric Constans A Lagrangian Simulation of the
Floating-Arm Trebuchet . . . . . . . . . 179--187
Ángel Plaza Proof Without Words: Sum of a Row in
Pascal's Triangle . . . . . . . . . . . 188--188
Carl V. Lutzer A Curious Feature of Regression . . . . 189--198
Maria Nogin Optimizing Prisms of All Shapes and
Dimensions . . . . . . . . . . . . . . . 199--203
Roger B. Nelsen Proof Without Words: Nested Square Roots 204--204
Krzysztof Chris Ciesielski and
David Miller On a Genocchi-Peano Example . . . . . . 205--213
Sam Northshield Two Short Proofs of the Infinitude of
Primes . . . . . . . . . . . . . . . . . 214--216
Arpan Sadhukhan Partitioning the Natural Numbers to
Prove the Infinitude of Primes . . . . . 217--218
Anonymous Problems and Solutions . . . . . . . . . 219--225
Bonnie Gold Book Review . . . . . . . . . . . . . . 226--232
Anonymous Media Highlights . . . . . . . . . . . . 233--240
Anonymous Editorial Board . . . . . . . . . . . . ??
Iwan Praton Minimal Tilings of a Unit Square . . . . 242--247
David Nacin Dihedoku Puzzle 1 . . . . . . . . . . . 248--248
Jonathan Needleman and
Felicia Sciortino UFOs in the game SET: Looking for
Airplanes and Spaceships . . . . . . . . 249--257
David Nacin Dihedoku Puzzle 2 . . . . . . . . . . . 258--258
Patrick J. Costello Tiling Squares with Big Holes with
$L$-trominoes . . . . . . . . . . . . . 259--263
David Nacin Dihedoku Puzzle 3 . . . . . . . . . . . 264--264
Mindy Capaldi and
Tiffany Kolba Carcassonne in the Classroom . . . . . . 265--273
David Nacin On a Complex KenKen Problem . . . . . . 274--282
David Nacin Dihedoku Puzzles Solutions . . . . . . . 283--283
David Betounes and
Mylan Redfern The Demise of Trig Substitutions? . . . 284--287
Katrina Eidolon and
Greg Oman A Short Proof of the
Bolzano--Weierstrass Theorem . . . . . . 288--289
Paul Carter and
Yitzchak Elchanan Solomon Relaxing the Integral Test: a Challenge
for the Advanced Calculus Student . . . 290--291
Anonymous Problems and Solutions . . . . . . . . . 292--301
Jason Rosenhouse Book Review . . . . . . . . . . . . . . 302--312
Anonymous Media Highlights . . . . . . . . . . . . 313--320
Anonymous Editorial Board . . . . . . . . . . . . ??
Brendan W. Sullivan and
Nikolas Townsend and
Mikayla L. Werzanski An Introduction to Lazy Cops and Robbers
on Graphs . . . . . . . . . . . . . . . 322--333
John Molokach Proof Without Words: The Pythagorean
Theorem . . . . . . . . . . . . . . . . 334--334
Li Zhou Did Elvis Know Cauchy--Schwarz? . . . . 335--338
Alda Carvalho and
Carlos Pereira dos Santos and
Jorge Nuno Silva The Geometer Dog Who Did Not Know
Calculus . . . . . . . . . . . . . . . . 339--345
Ángel Plaza Proof Without Words: a Pascal-Like
Triangle With Pell Number Row Sums . . . 346--346
Roger W. Johnson Bet(ch)a my Team Wins the Playoffs . . . 347--353
Alik Palatnik Proof Without Words: Varignon's Theorem 354--354
Óscar Ciaurri and
Emilio Fernández Variations on an Archimedean Ground: The
Generalized Salinon . . . . . . . . . . 355--365
Pietro Paparella A Short and Elementary Proof of the
Two-Sidedness of the Matrix Inverse . . 366--367
Wenti Zhong On the Eigenvalues of Anticommuting
Matrices . . . . . . . . . . . . . . . . 368--369
Anonymous Problems and Solutions . . . . . . . . . 370--377
Anne Quinn Technology Review: Statistics Web Apps 378--382
Anonymous Media Highlights . . . . . . . . . . . . 383--390
Anonymous George Pólya Awards for 2017 . . . . . . 391--392
Anonymous Notes on Volume 47 . . . . . . . . . . . 393--396
Anonymous Referees in 2017 . . . . . . . . . . . . 397--398
Anonymous Editorial Board . . . . . . . . . . . . ??
Stanley R. Huddy and
Michael A. Jones The Calculus Behind Generic Drug
Equivalence . . . . . . . . . . . . . . 2--9
Yukio Kobayashi Proof Without Words: a Sum Computed by
Self-Similarity . . . . . . . . . . . . 10--10
Vincent J. Matsko Designing Koch-Like Curves . . . . . . . 11--19
Allan Bickle MegaMenger Graphs . . . . . . . . . . . 20--26
Allan Berele and
Stefan Catoiu The Centroid as a Nontrivial Area
Bisecting Center of a Triangle . . . . . 27--34
Yajun An and
Tom Edgar Proof Without Words: Rearranged
Alternating Harmonic Series . . . . . . 35--35
Brittany A. Burke and
Zach Jackson and
Steven J. Kifowit The Falling Ladder Paradox Revisited . . 36--40
Haryono Tandra Basic Theorems in the Language of
Maximal Intervals . . . . . . . . . . . 41--45
Wm. Douglas Withers Triple Integrals for the
Sketching-Impaired . . . . . . . . . . . 46--53
Wojciech Kossek Is a Taylor Series also a generalized
Fourier Series? . . . . . . . . . . . . 54--56
Harvey Diamond The Rational Approximation of Small
Angles . . . . . . . . . . . . . . . . . 57--59
Anonymous Problems and Solutions . . . . . . . . . 60--67
Brigitte Servatius Book Review: \booktitleA Treatise of
Conic Sections by George Salmon, Hodges
and Smith, Dublin, 1848. Reprint of
sixth edition, American Mathematical
Society, Providence, RI, 2005. xv + 399
pp., ISBN 978-0-8218-3777-1, \$54.00
(hardback)} . . . . . . . . . . . . . . 68--72
Anonymous Media Highlights . . . . . . . . . . . . 73--80
Anonymous About the cover . . . . . . . . . . . . ??
Arthur T. Benjamin Factoring Numbers with Conway's 150
Method . . . . . . . . . . . . . . . . . 122--125
Mike Krebs Can a Subset's Topology Detect
Continuous Extensions? . . . . . . . . . 138--139
Anonymous Media Highlights . . . . . . . . . . . . 153--160
Dustin G. Mixon and
James Solazzo A Short Introduction to Optimal Line
Packings . . . . . . . . . . . . . . . . 82--91
Lucas Amiras Proof Without Words: Volume of a
Pedestal Prismoid . . . . . . . . . . . 92--92
William C. Mercier Why the Centroid is the Centroid: Modern
Variations on a Theme of Archimedes . . 93--102
Andrew Leahy A Fourth Century Theorem for
Twenty-First Century Calculus . . . . . 103--108
Peter McGrath Newton's Shell Theorem via Archimedes's
Hat Box and Single-Variable Calculus . . 109--113
Kevin P. Knudson Cutting Against the Grain: Volumes of
Solids of Revolution via Cross-Sections
Parallel to the Rotation Axis . . . . . 114--120
Tim Price Proof Without Words: Sum of Squares of
Consecutive Fibonacci Numbers . . . . . 121--121
David Salwinski Euler's Sine Product Formula: an
Elementary Proof . . . . . . . . . . . . 126--135
Esther M. García-Caballero and
Samuel G. Moreno The Double-Sidedness of Matrix Inverses;
Yet Another Proof . . . . . . . . . . . 136--137
Anonymous Problems and Solutions . . . . . . . . . 140--146
Brian Hopkins Book Review: \booktitleCombinatorics: a
Very Short Introduction by Robin Wilson,
Oxford University Press, Oxford, 2016,
xviii + 158 pp., ISBN 978-0-19-872349-3,
\$11.95 paperback, \$7.99 electronic.
\booktitleInfinity: a Very Short
Introduction by Ian Stewart, Oxford
University Press, Oxford, 2017, xvi +
144 pp., ISBN 978-0-19-875523-4, \$11.95
paperback, \$7.99 electronic . . . . . . 147--152
Anonymous About the Cover . . . . . . . . . . . . ??
Mehtaab Sawhney An Unusual Proof of the Triangle
Inequality . . . . . . . . . . . . . . . 218--218
Ezra Brown and
Matthew Crawford Five Families Around a Well: a New Look
at an Old Problem . . . . . . . . . . . 162--168
Jiang-Ping Jeff Chen A Systematic Treatment of ``Linear
Algebra'' in 17th-Century China . . . . 169--179
Stephan Berendonk Proof Without Words: Sums of Squares in
a Thin Rectangle . . . . . . . . . . . . 180--180
Burkard Polster and
Marty Ross Marching in Squares . . . . . . . . . . 181--186
Pedro J. Freitas and
Hugo Tavares Dividing the Circle . . . . . . . . . . 187--194
David Benko and
Dan Coroian A New Angle on the Fermat--Torricelli
Point . . . . . . . . . . . . . . . . . 195--199
Ángel Plaza Proof Without Words: an Alternating
Geometric Series . . . . . . . . . . . . 200--200
C. Ray Rosentrater Fakin' Flips . . . . . . . . . . . . . . 201--204
Roberta La Haye and
Petr Zizler The Gini Index and Grayscale Images . . 205--211
Granville Sewell Derivation of the Black--Scholes
Equation from Basic Principles . . . . . 212--215
Ajoy Thamattoor Normal Limit of the Binomial via the
Discrete Derivative . . . . . . . . . . 216--217
Jonathan Hoseana On Zero-Over-Zero Form Limits of a
Special Type . . . . . . . . . . . . . . 219--221
Anonymous Problems and Solutions . . . . . . . . . 222--228
Shirley B. Gray Book Review: \booktitleThe World of
Maria Gaetana Agnesi, Mathematician of
God by Massimo Mazzotti, The Johns
Hopkins University Press, Baltimore, MD,
2007. xx + 217 pp., ISBN
978-0-801-88709-3, \$56.95 (hardback);
2018, ISBN 978-1-421-42515-3, \$24.95
(paperback) . . . . . . . . . . . . . . 229--232
Anonymous Media Highlights . . . . . . . . . . . . 233--240
Anonymous About the cover . . . . . . . . . . . . ??
C. Douglas Howard It's Puzzling . . . . . . . . . . . . . 242--249
David Nacin Knightdoku Puzzle 1 . . . . . . . . . . 250--250
Erin Frassetto and
Michael Gableman and
McKenzie Lamb and
Tyler Shimek and
Andrea Young Strange Spinners and Diversity of Dice
in Chutes and Ladders . . . . . . . . . 251--260
David Nacin Knightdoku Puzzle 2 . . . . . . . . . . 261--261
Jonathan Hoseana Variations on the Binary Mind-Reading
Trick . . . . . . . . . . . . . . . . . 262--268
David Nacin Knightdoku Puzzle 3 . . . . . . . . . . 269--269
Sam Britton and
Joseph DiMuro and
Daniel Lundstrom and
Joshua Sansonetti Probabilities of Qwirkle Hand Values . . 270--276
David Nacin Knightdoku Puzzle 4 . . . . . . . . . . 277--277
Thomas M. Fiore and
Alexander Lang and
Antonella Perucca Tactile Tools for Teaching: Implementing
Knuth's Algorithm for Mastering
Mastermind . . . . . . . . . . . . . . . 278--286
David Nacin Knightdoku Puzzles Solutions . . . . . . 287--287
John P. Bonomo The Solution to a Hanoi-ing Little
Problem . . . . . . . . . . . . . . . . 288--291
Timothy McDevitt and
Angela Wesneski A Simple Probability Paradox . . . . . . 292--294
Anonymous Problems and Solutions . . . . . . . . . 295--301
Tom Edgar Roger Nelsen's Books, So Far . . . . . . 302--312
Anonymous Media Highlights . . . . . . . . . . . . 313--320
Anonymous About the cover . . . . . . . . . . . . ??
Brian Hopkins From the Editor: All Things Move . . . . 322--322
Douglas J. Shaw Harris Graphs --- a Graph Theory
Activity for Students and Their
Instructors . . . . . . . . . . . . . . 323--326
Roger B. Nelsen Further Integral Skinning with
Applications . . . . . . . . . . . . . . 327--332
Dirk Lorenz and
Karl-Joachim Wirths Sarrus Rules for Matrix Determinants and
Dihedral Groups . . . . . . . . . . . . 333--340
Gerald E. Bilodeau Proof Without Words: Riemann Meets
Euler--Mascheroni . . . . . . . . . . . 341--341
John Zacharias Proof of a Conjecture of Merca on an
Average of Square Roots . . . . . . . . 342--345
Shirley Gray and
Cye H. Waldman Archimedes Redux: Center of Mass
Applications from The Method . . . . . . 346--352
Poontarika Khotmongkon and
Nahathai Rerkruthairat and
Sujittra Suriwong and
Kornkanok Watcharakarn The Probability of Winning a Racquetball
Game with Deuce . . . . . . . . . . . . 353--358
D. N. Seppala-Holtzman A Canonical Conical Function . . . . . . 359--362
Artur Grygorian and
Ionut E. Iacob A Concise Proof of the Triangle
Inequality for the Jaccard Distance . . 363--365
Li Zhou Proof Without Words: Elvis Trades
Running for Swimming . . . . . . . . . . 366--366
Enrique Treviño An Inclusion-Exclusion Proof of Wilson's
Theorem . . . . . . . . . . . . . . . . 367--368
Tom Richmond Calculus with Curtains . . . . . . . . . 369--370
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 371--377
Brian P. Katz Book Review: \booktitleA TEXas-Style
Introduction to Proof by Ron Taylor and
Patrick X. Rault, MAA Press, Washington,
DC, 2017, xiv + 161 pp., ISBN
978-1-93951-213-0, \$50.00 paperback,
\$50.00 electronic.
\booktitleDiscovering Discrete Dynamical
Systems by Aimee S. A. Johnson, Kathleen
M. Madden, and Ayse A. Sahin, MAA Press,
Washington, DC, 2017, xiii + 116 pp.,
ISBN 978-0-88385-793-9, \$50.00
paperback, \$50.00 electronic . . . . . 378--383
Warren Page and
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 384--391
Anonymous George Pólya Awards for 2018 . . . . . . 392--394
Anonymous Notes on Volume 48 . . . . . . . . . . . 395--398
Anonymous Referees in 2018 . . . . . . . . . . . . 399--400
Anonymous About the cover . . . . . . . . . . . . ??
Dominic Klyve Letter from the Editor . . . . . . . . . 2--2
Mark Dalthorp When Fractions Make Cycles . . . . . . . 3--8
Harold P. Boas The Oldest Trig in the Book . . . . . . 9--20
Christopher J. Catone Bringing Calculus into Discrete Math via
the Discrete Derivative . . . . . . . . 21--27
Ian M. Adelstein and
George L. Ashline Reframing the Pythagorean Theorem . . . 28--35
Enrique Treviño A Birthday in St. Petersburg . . . . . . 36--40
Mark Sand Adding and Subtracting in the Cantor Set 41--45
David M. Bradley The Method of Determined Coefficients 46--53
Cesar Adolfo Hernandez Melo and
Fernanda Diniz de Melo Hernandez Uniform Continuity: Another Way to
Approach This Concept in the Classroom 54--57
R. Basu and
V. Kannan and
K. Sannyasi and
N. Unnikrishnan Functions Preserving Limit Superior . . 58--60
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 61--67
Brian Hopkins Book Review: \booktitlePythagorean
Triangles by Waclaw Sierpi\'nski, trans.
Ambikeshwar Sharma, Yeshiva University,
New York, 1962. Reprint, Dover, Mineola,
NY, 2013. viii + 72 pp., ISBN
978-0-486-43278-6, \$12.95 (paperback)} 68--72
Anonymous Media Highlights . . . . . . . . . . . . 73--80
Anonymous About the cover . . . . . . . . . . . . ??
Adam Glesser and
Matt Rathbun and
Isabel M. Serrano and
Bogdan D. Suceava Eclectic Illuminism: Applications of
Affine Geometry . . . . . . . . . . . . 82--92
Stephen Kaczkowski A Riemann Sum Approach to Buffon's
Needle . . . . . . . . . . . . . . . . . 93--102
Robert M. French and
Patrick Géhant The Barycenter Theorem: Averaging
Possible-Paths to Produce Optimal
Discrete Straight-line Segments . . . . 103--114
Juan Carlos Ponce Campuzano Conics as Envelopes of Families of Plane
Curves . . . . . . . . . . . . . . . . . 115--122
Jean-Paul Truc Riemann Sums for Generalized Integrals 123--132
Kenneth Mulder Geek Tragedy . . . . . . . . . . . . . . 133--133
Zarema Seidametova and
Valerii Temnenko Euler's Insignia: Some Admirable Curves
Having a Simple Trigonometric Equation
in a Natural Form . . . . . . . . . . . 134--139
Yusuf Z. Gurtas An Alternative to Integration by Partial
Fractions Technique . . . . . . . . . . 140--142
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 143--149
Scott Guthery Book Review: \booktitleLost in Math: How
Beauty Leads Physics Astray by Sabine
Hossenfelder: Basic Books, New York,
2018. 304 pp., ISBN 978-0-465-09425-7,
\$20.40} . . . . . . . . . . . . . . . . 150--152
Anonymous Media Highlights . . . . . . . . . . . . 153--160
Anonymous About the cover . . . . . . . . . . . . ??
Vlastimil Dlab and
Kenneth S. Williams The Many Sides of the Pythagorean
Theorem . . . . . . . . . . . . . . . . 162--172
Richard Goldstone and
Robert Suzzi Valli Unfoldings of the Cube . . . . . . . . . 173--184
Alvin Penner Fitting a Cubic Bézier to a Parametric
Function . . . . . . . . . . . . . . . . 185--196
Samuel G. Moreno and
Esther M. García-Caballero Proof Without Words: Sophie Germain's
Identity . . . . . . . . . . . . . . . . 197--197
Trienko Grobler Visualization of the Riemann--Stieltjes
Integral . . . . . . . . . . . . . . . . 198--209
Andrew J. Simoson Extrapolating Plimpton 322 . . . . . . . 210--220
Pisamai Kittipoom A Remark on Variation of Parameters . . 221--223
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 224--232
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 233--240
Anonymous About the cover . . . . . . . . . . . . ??
John Engbers and
Adam Hammett The $n$-Children Problem . . . . . . . . 242--249
Douglas Lyman Corey and
Jacob Badger and
Steven Lauzon Spirals, Triangles, and Tie-Dyed
T-Shirts . . . . . . . . . . . . . . . . 250--259
William W. Miles and
Sammi E. Smith The Choking Index: An Analysis of
Performance Under Pressure on the PGA
Tour . . . . . . . . . . . . . . . . . . 260--271
Kevin L. T. Chan and
Wai-Sum Chan Developing an Optimal Strategy for a
Maximization Dice Game . . . . . . . . . 272--279
Yajun An and
Tom Edgar ``Sum'' Visual Rearrangements of the
Alternating Harmonic Series . . . . . . 280--285
David Richeson By the Numbers . . . . . . . . . . . . . 286--287
William Paulsen Greedy Queens on an Infinite Chessboard 288--294
Michael A. Jones and
Jennifer Wilson A Two-Dimensional Perspective on
Simpson's Paradox and Its Likelihood . . 295--297
Suk-Geun Hwang and
Ik-Pyo Kim Orientation of the Cross Product of
$3$-vectors . . . . . . . . . . . . . . 298--299
David Richeson By the Numbers Solution . . . . . . . . 300--300
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 301--306
David Richeson Book Review: \booktitleCalculus
Reordered: A History of the Big Ideas by
David Bressoud, Princeton University
Press, Princeton, 2019. \booktitleChange
Is the Only Constant: The Wisdom of
Calculus in a Madcap World by Ben Orlin,
Black Dog & Leventhal, New York, 2019.
\booktitleInfinite Powers: How Calculus
Reveals the Secrets of the Universe by
Steven Strogatz, Houghton Mifflin
Harcourt, Boston, 2019 . . . . . . . . . 307--312
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 313--320
Anonymous About the cover . . . . . . . . . . . . ??
Elias Abboud and
Fathi Saleh and
Amal-Sharif Rasslan Coloring a $1$-by-$n$ Chessboard . . . . 322--330
C. Bryan Dawson Calculus Limits Unified and Simplified 331--342
Lindsey Bell and
Rachel Wagner Modeling Emergency Room Arrivals Using
the Poisson Process . . . . . . . . . . 343--350
Albert Natian Pinpoint the Flitting Fly . . . . . . . 351--356
Andrea Gasparini and
Eric Key and
David Radcliffe A Geometric Approach to the Natural
Exponential Function . . . . . . . . . . 357--363
Arman Maesumi Triangle Inscribed-Triangle Picking . . 364--371
Sylvia Carlisle and
William R. Green Solving systems of differential
equations in the case of a defective
coefficient matrix . . . . . . . . . . . 372--374
John P. Millis and
Courtney K. Taylor Areas of a Total Eclipse . . . . . . . . 375--377
Roger B. Nelsen Proof Without Words: Pythagorean Primes
and Triangular Numbers . . . . . . . . . 378--378
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 379--384
Jean Marie Linhart The Art of Logic in an Illogical World 385--388
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 389--396
Anonymous George Pólya Awards for 2019 . . . . . . 397--398
Anonymous Erratum . . . . . . . . . . . . . . . . 399--399
Anonymous About the cover . . . . . . . . . . . . ??
Anonymous Referees in 2019 . . . . . . . . . . . . ??
Anonymous About the cover . . . . . . . . . . . . ??
Anonymous Letter from the Editor . . . . . . . . . 2--2
William Dunham A Morsel from Euler . . . . . . . . . . 3--8
Tom Edgar Visual Decompositions of Polygonal
Numbers . . . . . . . . . . . . . . . . 9--12
David Pengelley From Lecture to Active Learning: Rewards
for All, and Is It Really So Difficult? 13--24
Semyon Litvinov and
Frantisek Marko Sums of Powers of Consecutive Integers
and Pascal's Triangle . . . . . . . . . 25--31
Samuel Durham and
Tom Richmond Connected Subsets of an $ n \times 2 $
Rectangle . . . . . . . . . . . . . . . 32--42
Kevin Y. Du A Fast-Growing Sequence Inspired by
TREE(k) . . . . . . . . . . . . . . . . 43--50
Dominic Klyve 50 Years of CMJ: The First Decade . . . 51--52
Richard Kaufman Limits on Legs of Pythagorean Triples
and Fermat's Last Theorem . . . . . . . 53--56
Zarema Seidametova and
Valerii Temnenko Some Geometric Objects Related to a
Classical Problem of Galileo . . . . . . 57--65
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 66--72
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 73--80
Anonymous About the cover . . . . . . . . . . . . ??
Francesco Ciraulo and
Samuele Maschio Solving Knights-and-Knaves with One
Equation . . . . . . . . . . . . . . . . 82--89
David Treeby Randomly Generated Identities . . . . . 90--94
J. M. Christian and
H. A. J. Middleton-Spencer On the $N$ th Roots of $ - 1$ and
Complex Basin Boundaries: Fractals from
Newton--Raphson . . . . . . . . . . . . 95--104
John Eggers A Closer Look at the Compensating Polar
Planimeter . . . . . . . . . . . . . . . 105--116
John Engbers and
Adam Hammett To Replace or Not to Replace --- That is
the Question . . . . . . . . . . . . . . 117--123
Sergiy Koshkin Bisecting Horn Angles . . . . . . . . . 124--131
Jeffrey Lawson and
Matthew Rave Sweeping Gestures: A Control Theory
Model for Curling . . . . . . . . . . . 132--140
M. G. Mahmoudi The AM-GM Inequality via Gradient . . . 141--143
Warren Page The (Two-Year) College Mathematics
Journal during the 1980s . . . . . . . . 144--145
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 146--152
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 153--160
Anonymous About the cover . . . . . . . . . . . . ??
Dan May and
Dan Swenson The Proportion of Comets in the Card
Game SET . . . . . . . . . . . . . . . . 162--172
Stan Wagon Counting Connected Sets of Squares . . . 173--173
Brian D. Jones Chance Encounters with Large Polynomials 174--181
Claire Kiers The Dynamics of the Greenhouse Effect 182--194
Barry S. Fagin Idempotent Factorizations in the
Cryptography Classroom . . . . . . . . . 195--203
Milton F. Maritz and
Mar\`et Cloete Fold-over Regions in Nonlinear First
Order PDEs . . . . . . . . . . . . . . . 204--215
Ann E. Watkins and
William Watkins The \booktitleCollege Mathematics
Journal during the 1990s . . . . . . . . 216--217
Francesco Laudano Proof Without Words: Magic of Tangential
Polygons . . . . . . . . . . . . . . . . 218--218
Michael A. Brilleslyper Unimodular Roots of Quadrinomials . . . 219--221
Donald L. Muench The Last Two Days in Elementary Linear
Algebra . . . . . . . . . . . . . . . . 222--224
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 225--232
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 233--240
Anonymous About the cover . . . . . . . . . . . . ??
Steve Bacinski and
Timothy Pennings How to Win at Tenzi . . . . . . . . . . 242--253
Gary Kennedy Flattening the Curve . . . . . . . . . . 254--259
Dan Flath Derivatives Are Multipliers . . . . . . 260--270
Joaquim Nogueira and
Fátima Rodrigues and
Luís Trabucho Some Probability Calculations Concerning
the Egyptian Game Senet . . . . . . . . 271--283
Leonid Hanin A Tour of Discrete Probability Guided by
a Problem in Genomics . . . . . . . . . 284--294
Chungwu Ho and
Gregory Mellblom and
Marc Frodyma On the Sum of Powers of Consecutive
Integers . . . . . . . . . . . . . . . . 295--301
Lowell Beineke The \booktitleCollege Mathematics
Journal during the Decade of the 2000s 302--303
Günhan Caglayan Proof Without Words: Sums of Polygonal
Numbers . . . . . . . . . . . . . . . . 304--304
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 305--312
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 313--320
Anonymous About the cover . . . . . . . . . . . . ??
John Conway and
Gabrielle Agus and
David Slusky Converting Between Dates in the Hebrew
and Roman Calendars . . . . . . . . . . 322--329
Adam Hammett Euler's Limit and Stirling's Estimate 330--336
J. Marshall Ash Discontinuous Functions as Limits of
Compactly Supported Formulas . . . . . . 337--344
João Teixeira and
Maria João Borges Formula for the Computation of the
Matrix Exponential . . . . . . . . . . . 345--350
Mervlyn Moodley Matrix Solution to Gergonne's Pile
Problem . . . . . . . . . . . . . . . . 351--357
Brian Hopkins The Fifth Decade of the CMJ . . . . . . 358--359
Paul Laumakis Analyzing Proportionality Coefficients
in Differential Equation Models . . . . 360--368
Anonymous George Pólya Awards for 2020 . . . . . . 369--370
Günhan Caglayan Proof Without Words: Centered Nonagonal
Numbers are Triangular . . . . . . . . . 371--371
William R. Green The Natural Frequency: More Natural and
More Frequent than Expected . . . . . . 372--374
Michael A. Jones A Difference Equation Approach to Finite
Differences of Polynomials . . . . . . . 375--377
Oksana Rubis and
Kathleen M. Clark Book Review: \booktitleA Guide to Higher
Learning by Julie Chen, Flying Fish
Press, Oakland, 2009 . . . . . . . . . . 378--384
Stephan Berendonk Geometric Series in an Equilateral
Triangle --- Three Proofs Without Words 385--385
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 386--392
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 393--400
Anonymous Referees in 2020 . . . . . . . . . . . . ??
Anonymous About the Cover . . . . . . . . . . . . ??
Darrin Frey and
Adam Hammett An Infinite Family of Divisibility Tests 2--10
Phillip H. Schmidt Two Friends and a Bike . . . . . . . . . 11--21
Miguel A. Lerma Truck Versus Human 2.0: Mathematical
Follow-Up Under Increasing Pressure, and
How Kepler's Laws Come to the Rescue . . 22--30
Andrzej Piotrowski Atypical Series Representations of
Riemann-Integrable Functions . . . . . . 31--38
Wenjie Wang The Explicit Expression of Axis and
Angle of a Rotation Matrix . . . . . . . 39--44
Anurag Agarwal and
David L. Farnsworth and
Carl V. Lutzer and
James E. Marengo and
J. A. Stephen Viggiano Extremal Correlation Coefficients for
Bivariate Probability Distributions with
Specified Marginal Distributions . . . . 45--53
José Ángel Cid An Excursion Through the Double
Sidedness of the Matrix Inverse . . . . 54--56
Peter A. Loeb Chain Rule Note . . . . . . . . . . . . 57--58
Jean Marie Linhart Mathematics for Human Flourishing . . . 59--63
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 64--72
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 73--80
Anonymous About the Cover . . . . . . . . . . . . ??
Steven J. Miller and
Haoyu Sheng and
Daniel Turek When Rooks Miss: Probability through
Chess . . . . . . . . . . . . . . . . . 82--93
Michael Schmitz A Plea for Finite Calculus . . . . . . . 94--105
Steven Beres and
Vesta Coufal and
Kate Kearney and
Ryan Lattanzi and
Hayley Olson Linking Numbers of Klein Links . . . . . 106--114
Sanja Stevanovi and
Dragan Stevanovi\'c Visual Proofs for the Sums of Fourth and
Fifth Powers of the First $n$ Natural
Numbers . . . . . . . . . . . . . . . . 115--120
Richard Goldstone and
Rachel Roca and
Robert Suzzi Valli Shortest Paths on Cubes . . . . . . . . 121--132
Tom Edgar Visual Triangular Number Identities from
Positional Number Systems . . . . . . . 133--136
Michael N. Fried An Observation about First-Order Linear
ODEs . . . . . . . . . . . . . . . . . . 137--139
Gary R. Lawlor An Eigenargument for Irrational Roots 140--141
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 142--148
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 149--156
Anonymous About the Cover . . . . . . . . . . . . ??
Scott Chapman and
Pedro García-Sánchez and
Christopher O'Neill Distances between Factorizations in the
Chicken McNugget Monoid . . . . . . . . 158--176
Aaron Montgomery What's in the Bag? . . . . . . . . . . . 177--184
Adrian Rice and
Ezra Brown Why Hamilton Couldn't Multiply Triples 185--192
William Paulsen The Sock Problem Revisited . . . . . . . 193--203
Ivica Martinjak and
Ana Mimica Proofs Without Words: a Visual Proof for
an Infinite Alternating Sign Series . . 204--204
Antonio J. Moreno Verdejo and
Abraham López Viveros \ and
Rafael Ramirez Uclés Statistical Significance of the Median
of a Set of Points on the Plane . . . . 205--218
Melanie Tian and
Enrique Treviño An Unusual Recursive Formula to Answer a
Question Regarding Fixed Points in
Permutations . . . . . . . . . . . . . . 219--220
Georgios Passias and
Sven-Ake Wegner On a Counterexample in Connection with
the Picard--Lindelöf Theorem . . . . . . 221--223
Brian Becsi and
Solomon Huang and
Verenalei Schoenfeld and
Bogdan D. Suceava \ and
Ashley Thune-Aguayo Applications of Squeeze Theorem to
Limiting Processes Involving Riemann
Integration . . . . . . . . . . . . . . 224--226
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 227--232
Tanya Leise Media Highlights . . . . . . . . . . . . 233--240
Anonymous Correction . . . . . . . . . . . . . . . 241--241
Anonymous About the Cover . . . . . . . . . . . . ??
Oscar Levin and
Tyler Markkanen Puzzles of Cardinality . . . . . . . . . 243--253
Joshua Carlson and
Alex Christensen and
Pamela E. Harris and
Zakiya Jones \ and
Andrés Ramos Rodríguez Parking Functions: Choose Your Own
Adventure . . . . . . . . . . . . . . . 254--264
John P. Bonomo Back to the Tower . . . . . . . . . . . 265--273
Richard Ehrenborg Fano, Galois, Hamming and a Card Trick 274--280
Hideo Nagahashi Magic Card Tricks on Hamming Codes over
Finite Fields . . . . . . . . . . . . . 281--288
Thomas J. Clark Classroom and Computational
Investigations of \em Camel Up . . . . . 289--296
Xiaoyan Hu Proof Without Words: Center of Mass . . 297--297
Dennis L. Sun Proof Without Words: Convex Hulls and
Jensen's Inequality . . . . . . . . . . 298--298
Greg Orosi and
Ricardo Alfaro and
Lixing Han and
Kenneth Schilling An Elementary Derivation of the Duration
of Play in the Gambler's Ruin Problem 299--301
Yves Nievergelt Is Doom the Inescapable Solution of
Initial Value Problems? . . . . . . . . 302--305
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 306--315
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 316--323
Anonymous Correction . . . . . . . . . . . . . . . ??
Anonymous About the Cover . . . . . . . . . . . . ??
Matt Davis and
Adam E. Parker and
Daniel A. N. Vargas Being Rational About Algebraic Numbers 327--337
Tiffany N. Kolba and
Jonathan Beagley Counting Christmas Trees . . . . . . . . 338--344
Hou-Biao Li and
Hong Li and
Ting-Zhu Huang Chaos in Determinant Condensation
Calculations . . . . . . . . . . . . . . 345--354
Roger Nelsen Machin's Formula Via a Proof Without
Words . . . . . . . . . . . . . . . . . 355--355
Samantha Pezzimenti and
Giovanni DiCicco and
Aditya Kommoju \ and
Dhanush Rajesh Exploring and Extending the Impossible
Card Location Trick . . . . . . . . . . 356--363
Joseph Previte and
Michelle Previte The Beautiful Chaotic Dynamics of $ i^z
$ . . . . . . . . . . . . . . . . . . . 364--372
Aniket Sanghi Visualizing the Complex Roots of
Quadratic and Cubic Polynomial Functions
in Three Dimensions . . . . . . . . . . 373--379
Edward A. Roualdes and
Neil C. Schwertman Optimal Pooling of COVID-19 Samples . . 380--384
Anonymous George Pólya Awards for 2021 . . . . . . 385--387
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 388--396
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 397--404
Anonymous Referees in 2021 . . . . . . . . . . . . ??
Robert Gallant and
Georg Gunther Arranging Beetles . . . . . . . . . . . 3--12
Béla Bajnok and
Evan Chen Report on the 12th Annual USA Junior
Mathematical Olympiad . . . . . . . . . 13--20
Judit Kardos Constructing Continuous Functions . . . 21--32
Mircea Merca Connections Between Partitions and
Divisors Related to the Parity of the
Partition Function . . . . . . . . . . . 33--37
Claudi Alsina and
Roger Nelsen Proof Without Words: Another Pythagorean
Theorem . . . . . . . . . . . . . . . . 38--38
Michael Maltenfort The Associativity of Infinite Matrix
Multiplication, Revisited . . . . . . . 39--44
Tom Edgar Visual Sums of Integers in Polygonal
Arrays . . . . . . . . . . . . . . . . . 45--51
Jay Mehta A Short Generalized Proof of Infinitude
of Primes . . . . . . . . . . . . . . . 52--53
Angel S. Muleshkov and
Kurt R. Sweat Elementary Functions . . . . . . . . . . 54--63
Yuanting Lu Using Linear Interpolation to Implement
the Change of Variables in Double
Integrals . . . . . . . . . . . . . . . 64--66
Howard Sporn A Proof of the Reflective Property of
the Parabola . . . . . . . . . . . . . . 67--68
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 69--76
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 77--84
Anonymous About the Cover . . . . . . . . . . . . ??
Robert L. Sachs Similarities in a First Differential
Equations Course . . . . . . . . . . . . 87--97
Zsolt Lengvárszky and
Tibor Szarvas The Law of Cosines with Differential
Calculus and Without . . . . . . . . . . 98--103
Johnner Barrett Unlawful Calculations: A Look Into Lie's
Notebook . . . . . . . . . . . . . . . . 104--115
Brian Johnson and
Lorna Wenzel Using the Intermediate Value Theorem to
Circumscribe Hyperbolic Triangles . . . 116--121
William Q. Erickson Haste Makes Waste: An Optimization
Problem . . . . . . . . . . . . . . . . 122--133
Yusuf Z. Gürtas An Unorthodox Approach to Skinning a
Definite Integral . . . . . . . . . . . 134--139
John A. Quintanilla A New Derivation of Snell's Law Without
Calculus . . . . . . . . . . . . . . . . 140--145
Alik Palatnik and
Moshe Stupel Proof Without Words: A Property of a
Cyclic Polygon with an Even Number of
Vertices . . . . . . . . . . . . . . . . 146--146
Emmanuel Antonio José García A Variant of the Eyeball Theorem . . . . 147--148
Peter R. Mercer Extending Extending Bernoulli's
Inequality . . . . . . . . . . . . . . . 149--150
Eli Leher On the Two ``Dimension Theorems'' . . . 151--151
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 152--160
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 161--168
F. M. S. Lima and
P. G. F. Jordão Why is it that the Ratio of Any Circle's
Circumference to its Diameter is a
Constant? . . . . . . . . . . . . . . . 171--182
James Blackburn-Lynch Are We Ever Our Best Possible Selves? An
Application of Bézout's Identity to Find
Coincident Peaks of Multiple Sine Curves 183--189
Henry Ricardo The Equivalence of Definitions of the
Natural Logarithm Function . . . . . . . 190--196
James N. Brawner and
Nadou Lawson Integer Solutions to Angle Optimization
Problems . . . . . . . . . . . . . . . . 197--208
Abe Edwards and
Brielle Komosinski Tetration: Iterative Enjoyment . . . . . 209--219
Steven J. Miller and
Enrique Treviño On the Sum of $k$ -th Powers in Terms of
Earlier Sums . . . . . . . . . . . . . . 220--225
Roger Nelsen Proof Without Words: Tangents of
Multiples of \pi /24 . . . . . . . . . 226--226
Juan Tolosa Two Eigenvectors for the Price of One 227--229
Pisheng Ding Less Mundane Applications of the Most
Mundane Functions . . . . . . . . . . . 230--232
Hanumant Singh Shekhawat Correlation and Subtraction . . . . . . 233--234
Allison Henrich \booktitleHow to Get Your PhD: A
Handbook for the Journey by Gavin Brown 235--236
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 237--244
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 245--252
David Nacin \em Kleinian KenKen . . . . . . . . . . 253--264
Genevieve Ahstrom and
Thomas Q. Sibley Fantasy on a Baseball Seam . . . . . . . 265--272
Jathan Austin and
Emelie Curl Exploring Combinatorics and Graph Theory
with Simple Blokus . . . . . . . . . . . 273--281
Jason Imbrogno and
David Bergman Computing the Number of Winning NFL
Survivor Pool Entries . . . . . . . . . 282--291
Hiroshi Okumura A sangaku problem involving two circles
and an equilateral triangle . . . . . . 292--297
Michael A. Jones and
Aidan Shor and
Jennifer Wilson Allocating Scarce Resources using a
Weighted Lottery . . . . . . . . . . . . 298--305
Wayne Nirode and
Norm Krumpe Donuts with Pythagoras . . . . . . . . . 306--311
Aaron Melman An Exclusion Sector for Zeros of
Polynomials with Nonnegative
Coefficients . . . . . . . . . . . . . . 312--314
Peter B. Gothen and
António Guedes de Oliveira On the classification of the rigid
motions of the plane . . . . . . . . . . 315--317
Roger Nelsen Proof Without Words: Consecutive
Powerful Numbers . . . . . . . . . . . . 318--318
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 319--325
Anonymous Media Highlights . . . . . . . . . . . . 326--333
Anonymous Correction . . . . . . . . . . . . . . . 334--334
Anonymous About the Cover . . . . . . . . . . . . ??
Cameron G. Hale and
Jonathan R. Kelleher and
John C. Mayer Multiplicity of Hexagon Numbers . . . . 335--346
Anonymous George Pólya Awards for 2022 . . . . . . 347--350
Sandy Norman and
Priya V. Prasad Variations on a Theorem of Varignon . . 351--360
Jeremiah W. Johnson A Diophantine Equation with an
Elementary Solution . . . . . . . . . . 361--363
Lindsey Bell and
Paul Hill An Investigation of Metropolitan Crime
Distribution . . . . . . . . . . . . . . 364--371
Michael Schmitz and
André Streicher Envelopes are Solving Machines for
Quadratics and Cubics and Certain
Polynomials of Arbitrary Degree . . . . 372--381
Dan Swenson A Statistics-Related Approach to the
Legislative Apportionment Problem \ldots
and also, a Second One . . . . . . . . . 382--391
Christian Aebi and
Grant Cairns A Vector Identity for Quadrilaterals . . 392--393
Yaakov Malinovsky A Short Probabilistic Proof of a
Binomial Identity . . . . . . . . . . . 394--395
William Y. C. Chen Cubic Equations Through the Looking
Glass of Sylvester . . . . . . . . . . . 396--398
Jonathan Balsam Proof Without Words: Lagrange's
Trigonometric Identity . . . . . . . . . 399--399
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 400--407
Tanya Leise and
Philip Straffin (Section Editor) Media Highlights . . . . . . . . . . . . 408--415
Anonymous Referees in 2022 . . . . . . . . . . . . 416--417
Anonymous About the Cover . . . . . . . . . . . . ??
Brian S. Thomson A Note on Teaching the Riemann Integral 3--10
David Treeby and
Marty Ross A Curious Property of Tangents . . . . . 11--14
Béla Bajnok Report on the 13th Annual USA Junior
Mathematical Olympiad . . . . . . . . . 15--21
David McCune A Simple Algorithm for Drawing
Apportionment Diagrams . . . . . . . . . 22--32
Damiano Fulghesu and
James A. Sellers and
Courtney K. Taylor Infinite Families of Infinite Series
With Integer Sums . . . . . . . . . . . 33--43
Christopher Ennis and
John Shier Disjoint Placement Probability of Line
Segments via Geometry . . . . . . . . . 44--53
Abdel Missa An Intuitive Method to Solve Quadratic
Equations . . . . . . . . . . . . . . . 54--61
Rex H. Wu Proof Without Words: a Geometric Series
through the Dissection of Regular
Hexagons . . . . . . . . . . . . . . . . 62--62
Günhan Caglayan Covering a Star Number with Pentagonal
Numbers . . . . . . . . . . . . . . . . 63--63
Grady Weyenberg Do Dogs Know Calculus With Early
Transcendentals? . . . . . . . . . . . . 64--67
Dr. Ricardo E. Rojas When Triangles Are Similar . . . . . . . 68--69
Editors Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 70--71
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 72--79
Anonymous About the Cover . . . . . . . . . . . . ??
William Dunham Bryn Mawr College Matriculation Exams
from a Century Ago . . . . . . . . . . . 83--89
Serge D'Alessio Solutions of the Van der Pol Equation 90--98
Michele Gaeta and
Giovanni Vincenzi Examples of Pairs of Ordered
Congruent-like $n$-gons with Different
Areas . . . . . . . . . . . . . . . . . 99--103
Romain Boulet Solving Linear Systems with Column
Reduction . . . . . . . . . . . . . . . 104--112
Tom Richmond and
Mia Sword An Arithmetic Triangle Arising From a
One-Way Street Grid . . . . . . . . . . 113--122
Seán M. Stewart On that most over Skinned of Improper
Integrals . . . . . . . . . . . . . . . 123--129
Matthew N. Moore An Elementary Treatment of the
Lambert-$W$ Relation . . . . . . . . . . 130--138
Rex H. Wu Proof Without Words: The Sum of Even
Powers of Three . . . . . . . . . . . . 139--139
Bikash Chakraborty and
Sagar Chakraborty A Generalization of Euler's Limit . . . 140--141
Semyon Litvinov and
Frantisek Marko Two Comments on the Binomial Theorem . . 142--144
Benjamin A. Lotto An Elementary Proof that Reduced Row
Echelon form of a Matrix is Unique . . . 145--146
Editors Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 147--160
Tanya Leise and
Philip Straffin Media Highlights . . . . . . . . . . . . 161--168
Anonymous About the Cover . . . . . . . . . . . . ??
Peter Gothen and
António Guedes de Oliveira On Euler's Rotation Theorem . . . . . . 171--175
Tom Edgar Balancing the Square Root of Two . . . . 176--178
David Aldous Exploring Endless Space . . . . . . . . 179--185
Molly Moran and
Jessica Schenkman Knot Theory in Linear Algebra: an
Example with Trip Matrices . . . . . . . 186--194
Greg Markowsky and
David Treeby Trigonometric Angle-Sum Formulas and
Conformal Maps . . . . . . . . . . . . . 195--199
Robert Graff and
Kelly Jabbusch and
David James Intuitive Interpretations of SVD Vectors 200--211
Jacob Brown Counting Divisions of a $ 2 \times n $
Rectangular Grid . . . . . . . . . . . . 212--221
Gregor Cigler and
Marjan Jerman Modifying Jordan Bases . . . . . . . . . 222--231
Katiuscia Teixeira Improper Integrals: an Alternative
Criterion . . . . . . . . . . . . . . . 232--234
Jonathan Balsam Proof Without Words: Lagrange's
Trigonometric Identity (Part II) . . . . 235--235
Tanya Leise (Section Editor, 2019--2023, In Memoriam) and
Philip Straffin Media Highlights . . . . . . . . . . . . 243--250
Anonymous About the Cover . . . . . . . . . . . . ??
Don Chakerian and
Stephen Erfle Up the Hill and Down Again . . . . . . . 256--268
Howard Sporn Forringer's Method and More Trees of
Pythagorean Triples . . . . . . . . . . 269--273
John P. Bonomo and
Montana Ferita A Small Fib . . . . . . . . . . . . . . 274--289
Jay Bartroff Rebalance Your Portfolio Without Selling 290--298
Stijn Dierckx An Extension of the Perplexing
Polynomial Puzzle . . . . . . . . . . . 299--307
Tevian Dray Hyperbolic Lunes . . . . . . . . . . . . 308--315
Hayden Ruff and
Kenneth Schilling An Attractive Attractor . . . . . . . . 316--325
Thunwa Theerakarn On the Center of Surface Area of the
Boundary of a Star-Shaped Region . . . . 326--336
James S. Wolper Not Solving Differential Equations . . . 337--344
David A. Nash A New Take on Classic `Pen Problems' . . 345--354
Jathan Austin and
Brian G. Kronenthal and
Jonathon Miller and
Susanna Molitoris-Miller Caught ``Red''-Handed? The Probability
of Randomly Constructing a Legal \em
Catan Board . . . . . . . . . . . . . . 355--366
Daniel J. Velleman Integration by Substitution: a Case
Study in the Relationship Between
Calculus and Analysis . . . . . . . . . 367--373
Melissa Holly Large Independent Set vs. Large Clique 374--377
Jyotirmoy Sarkar The Largest Quadrilateral is Cyclic: a
New Geometric Proof . . . . . . . . . . 378--384
Armengol Gasull Proof Without Words: Tangent of $ \pi /
8 $ . . . . . . . . . . . . . . . . . . 385--385
Jean-Paul Truc How to Marry the Kernel and the Image 386--387
Ron Lycan Two Quasigroup Elements Can Commute With
Any Positive Rational Probability . . . 388--390
Peter M. Higgins Limiting Behaviour of Pairs with Equal
Images for Polynomial Functions . . . . 391--393
Editors Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 394--399
Editors Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 400--405
Lowell Beineke and
Philip Straffin Media Highlights . . . . . . . . . . . . 406--413
Anonymous Correction . . . . . . . . . . . . . . . 414--414
Anonymous About the Cover . . . . . . . . . . . . ??
Daniel Solow Half an Induction Proof of the Collatz
Conjecture . . . . . . . . . . . . . . . 419--422
Michelle Cordier and
Meaghan Wheeler Searching for Point Locations Using
Lines . . . . . . . . . . . . . . . . . 423--433
Otis F. Graf Jr. Why the Golden Spiral is Golden . . . . 434--445
Osvaldo Marrero and
Paul C. Pasles The Multivariate Probabilistic Josephus
Problem . . . . . . . . . . . . . . . . 446--453
Alexander Holley and
Anastasiia Minenkova A Linear Algebra Story: How We
Reconstructed a Matrix from its
Eigenvalues . . . . . . . . . . . . . . 454--463
Sara Barrows and
Emily Noye and
Sarah Uttormark and
Matthew Wright Three's A Crowd: an Exploration of
Subprime Tribonacci Sequences . . . . . 464--475
Ellen Lehet and
Kuo-Liang Chang A Novel Method for Completing the Square 476--480
James Schultz Proof Without Words: The American Flag
Inspires a Proof that the Sum of the
First $n$ Positive Odd Integers is $
n^2$ . . . . . . . . . . . . . . . . . . 481--481
Roger Nelsen The Hermite--Hadamard Inequalities and
Applications . . . . . . . . . . . . . . 482--484
Howard Sporn The Golden Circle and the Aureate Circle 485--491
Greg Oman and
Charles N. Curtis Problems and Solutions . . . . . . . . . 492--499
Lowell Beineke Section Editor and
Philip Straffin Media Highlights . . . . . . . . . . . . 500--507
Anonymous Referees in 2023 . . . . . . . . . . . . 508--509
Anonymous About the Cover . . . . . . . . . . . . ??
Tamara Lakins Letter from the Editor . . . . . . . . . 3--3
Milton F. Maritz and
Mar\`et Cloete Analysis and Visualization of Fractional
Reflections . . . . . . . . . . . . . . 4--11
Eric Constans and
Nicola Golfari How to Fold a Triangle: The Connection
between the Grashof Fourbar Linkage and
Pythagorean Triangles . . . . . . . . . 12--23
Adam Hammett and
Kevin Roper A Sterling Look at Stirling's Constant 24--31
Christopher Ennis and
Inge Helland Disjoint Placement Probability of Line
Segments via Induction . . . . . . . . . 32--39
S. H. Sathish Indika and
Lawrence M. Leemis Exact Expressions for Trigonometric
Functions . . . . . . . . . . . . . . . 40--45
Dan Lawson and
David Richeson Zig-Zag Paths and Neusis Constructions
of a Heptagon and a Nonagon . . . . . . 46--55
Günhan Caglayan Proof Without Words: a Relationship of
Pentagonal and Hexagonal Numbers . . . . 56--57
Günhan Caglayan Proof Without Words: a Relationship of
Heptagonal and Nonagonal Numbers . . . . 58--58
Lawrence Smolinsky Rearrangements of a Conditionally
Convergent Series Summing to Logarithms
of Natural Numbers . . . . . . . . . . . 59--61
Gary R. Lawlor The Product of Two Natural Numbers
Equals the Product of their GCD and LCM 62--63
Greg Oman and
Matyas Sustik and
Katherine Thompson Problems and Solutions . . . . . . . . . 64--65
Lowell Beineke Section Editor and
Jennifer Beineke and
Philip Straffin Media Highlights . . . . . . . . . . . . 66--73
Béla Bajnok and
Enrique Treviño Report on the 14th Annual USA Junior
Mathematical Olympiad . . . . . . . . . 74--82
Anonymous About the Cover . . . . . . . . . . . . ??
Tamara Lakins (Editor) Letter from the Editor . . . . . . . . . 85--85
Milton F. Maritz Extracting Pi from Chaos . . . . . . . . 86--99
Timo Tossavainen and
Pentti Haukkanen and
Jorma K. Merikoski and
Mika Mattila We Can Differentiate Numbers, Too . . . 100--108
Rus May The Weight of a Ten-Pound Bag of
Potatoes . . . . . . . . . . . . . . . . 109--116
Skip Garibaldi The Luckiest Strategy on Earth? A Better
Way to Buy Lottery Scratch-off Tickets 117--125
Cooper Young Cutting the Möbius Strip . . . . . . . . 126--133
Jason Snyder A Modern Spin on Archimedes' Quadrature
of the Parabola . . . . . . . . . . . . 134--139
Robert L. Lamphere How to Compute the Volumes of Hyperbolic
Solids of Revolution . . . . . . . . . . 140--152
Roger B. Nelsen An Introduction to the Jacobsthal
Numbers . . . . . . . . . . . . . . . . 153--158
Günhan Caglayan A Relationship of Triangular, Square and
Pentagonal Numbers . . . . . . . . . . . 159--160
Thomas E. Cooper Proof Without Words: Bisecting a
Quadrilateral's Perimeter . . . . . . . 161--161
John Ferdinands and
Timothy Ferdinands An Extension of Babbage's Theorem . . . 162--164
Vilmos Komornik and
Reinhard Schäfke A Simple Introduction to the Exponential
Function . . . . . . . . . . . . . . . . 165--168
Roger Nelsen Summing Squares and Cubes Using
Triangular Numbers . . . . . . . . . . . 169--171
Kyumin Nam Approximation of Pi Using Infinite
Series of Arcsine . . . . . . . . . . . 172--174
Greg Oman and
Mátyás A. Sustik and
Katherine Thompson Problems and Solutions . . . . . . . . . 175--179
Lowell Beineke Section Editor and
Jennifer Beineke and
Philip Straffin Media Highlights . . . . . . . . . . . . 180--187
Anonymous About the Cover . . . . . . . . . . . . ??
Tami Lakins Letter from the Editor . . . . . . . . . 191--191
Tova Brown and
Brody Johnson Pull-Back Cars: Vehicles for the
Instruction of Differential Equations 192--204
Sandy Ganzell and
Caroline VanBlargan Knots with Composite Colors . . . . . . 205--209
Armine Bagyan and
Donald Richards A Continuous-Time Markov Chain Model for
the Spread of COVID-19 . . . . . . . . . 210--214
R. Travis Kowalski On a Particular Particular Solution . . 215--225
Lucy Martinez and
Doron Zeilberger A Guide to the Risk-Averse Gambler and
Resolving the St. Petersburg Paradox
Once and For All . . . . . . . . . . . . 226--234
Michael A. Jones and
Allison Mocny and
Jennifer Wilson The Will Rogers Phenomenon and
Sequential Migration . . . . . . . . . . 235--244
Roger Nelsen Proof Without Words: Cousin Prime
Products Modulo 72 . . . . . . . . . . . 245--245
Rex H. Wu Proof Without Words: an Alternating
Geometric Series . . . . . . . . . . . . 246--246
Kenichi Hirose Computing Sums of Powers of Integers
with the Hockey-Stick Identity and the
Stirling Numbers . . . . . . . . . . . . 247--249
Ricardo E. Rojas Dr A Two-for-One Deal on Rational Triangles 250--252
Joseph Amal Nathan A Simple and Short Proof of $ \det (A B)
= \det (A) \det (B) $ . . . . . . . . . 253--254
Marshall Gordon Chen's and Kennedy's Harmonic Series
Proof as a Teaching Tool . . . . . . . . 255--256
Mark B. Villarino and
Joseph C. Várilly Archimedes' Revenge . . . . . . . . . . 257--259
Greg Oman and
Mátyás A. Sustik and
Katherine Thompson Problems and Solutions . . . . . . . . . 260--268
Lowell Beineke (Section Editor) and
Jennifer Beineke and
Philip Straffin Media Highlights . . . . . . . . . . . . 269--276
Anonymous About the Cover . . . . . . . . . . . . ??
Tamara Lakins Letter from the Editor . . . . . . . . . 279--279
Christopher Cericola and
Justus Curry and
Allison Henrich and
Mitchell Rask The Arc Unknotting Game . . . . . . . . 280--293
Jacob A. Siehler New Problems in Port-and-Sweep Solitaire 294--302
Matvey Borodin and
Eric Chen and
Aidan Duncan and
Tanya Khovanova and
Boyan Litchev and
Jiahe Liu and
Veronika Moroz and
Matthew Qian and
Rohith Raghavan and
Garima Rastogi and
Michael Voigt The Stable Marriage Problem and Sudoku 303--316
Francesco Grotto and
Antonella Perucca and
Tatjana Van Steenbergen Bergeron Rubik's Snakes on a Plane . . . . . . . 317--327
Brian D. Jones Taxicab Metric of a Different Kind . . . 328--335
Todd G. Will Pentagons with Permutable Angles . . . . 336--342
Michael N. Fried Proof Without Words: a Property of
Tangent Circles . . . . . . . . . . . . 343--343
Günhan Caglayan Dr Proof Without Words: a Pattern Block
Dissection to Square the Regular
Dodecagon . . . . . . . . . . . . . . . 344--345
J. A. Grzesik A Novel Derivation of the
Gregory--Leibniz Series for Pi . . . . . 346--348
Sarmad Abbasi An Explicit Version of Saidak's Argument
for the Infinitude of Primes . . . . . . 349--349
Anonymous Crossword Puzzle . . . . . . . . . . . . 350--351
Greg Oman (Editors) and
Mátyás A. Sustik and
Katherine Thompson Problems and Solutions . . . . . . . . . 352--362
Lowell Beineke Section Editor and
Jennifer Beineke and
Philip Straffin Media Highlights . . . . . . . . . . . . 363--370
Brendan Sullivan Crossword Puzzle Solution . . . . . . . 371--371