Last update:
Wed Nov 8 12:07:25 MST 2023
Phillip A. Griffiths Mathematics at the Turn of the
Millennium . . . . . . . . . . . . . . . 1--14
C. W. Groetsch The Commandant's Corollary . . . . . . . 15--23
Jerome Reiter Using Statistics to Determine Causal
Relationships . . . . . . . . . . . . . 24--32
James Case Paradoxes Involving Conflicts of
Interest . . . . . . . . . . . . . . . . 33--43
J. E. McClure Start Where They Are: Geometry as an
Introduction to Proof . . . . . . . . . 44--52
Jerzy Tyszkiewicz A Simple Construction for Tournaments
with Every k Players Beaten by a Single
Player . . . . . . . . . . . . . . . . . 53--54
Maria Suzuki Alternative Formulations of the Twin
Prime Problem . . . . . . . . . . . . . 55--56
Alexander Russell An Easy Reduction of an Isoperimetric
Inequality on the Sphere to Extremal Set
Theory . . . . . . . . . . . . . . . . . 57--59
Peter Malcolmson and
Frank Okoh Rings without Maximal Ideals . . . . . . 60--61
Thomas R. Hagedorn A Proof of a Conjecture on Egyptian
Fractions . . . . . . . . . . . . . . . 62--63
S. S. Demidov and
A. Shenitzer The Evolution of \ldots Two Letters by
N. N. Luzin to M. Ya. Vygodskii . . . . 64--82
Catalin Zara Problem 10774 . . . . . . . . . . . . . 83--83
Hadi Salmasian Problem 10775 . . . . . . . . . . . . . 83--83
Yongge Tian Problem 10776 . . . . . . . . . . . . . 83--83
Zafar Ahmed Problem 10777 . . . . . . . . . . . . . 83--83
Paul Bateman and
Dennis Eichhorn Problem 10778 . . . . . . . . . . . . . 83--83
Andrei Jorza Problem 10779 . . . . . . . . . . . . . 83--83
Kiran Kedlaya Problem 10780 . . . . . . . . . . . . . 84--84
John P. Robertson and
GCHQ Problems Group Elliptic Curves to the Rescue: 10612 . . 84--86
George E. Andrews and
John Henry Steelman and
G. L. Body and
D. Callan and
R. J. Chapman and
K.-W. Lau and
J. T. Lewis and
J. H. Lindsey II and
G. Lord and
J. G. Merickel and
Anchorage Math Solutions Group Rogers--Ramanujan Partitions: 10627 . . 86--86
George E. Andrews and
Kee-Wai Lau and
G. L. Body and
D. Callan and
R. J. Chapman and
G. Lord and
H.-J. Seiffert and
D. Zeilberger Partitions and Pentagonal Numbers: 10628 86--87
Frank Schmidt and
Peter Mork and
D. Beckwith and
D. Callan and
D. J. Chapman and
G. Lord and
C. C. Rousseau and
P. Simeonov and
J. H. Steelman Interrupted Partitions: 10629 . . . . . 87--88
David Callan and
Robin J. Chapman and
J. H. Lindsey, II and
D. Huang The Value of Primitive Words: 10636 . . 88--89
Marcin Mazur and
Roy Barbara and
J. Anglesio and
R. J. Chapman and
N. Lakshmanan and
J. Melville and
G. Peng and
C. R. Pranesachar and
GCHQ Problems Group Quadrilaterals in an Isosceles Triangle:
10653 . . . . . . . . . . . . . . . . . 89--91
Michael Golomb and
GCHQ Problems Group and
G. D. Chakerian and
R. J. Chapman and
J. H. Lindsey II and
O. P. Lossers and
A. Nijenhuis Points That Form Simplices of Equal
Volume: 10685 . . . . . . . . . . . . . 91--91
John P. Pratt Book Review: \booktitleMapping Time: The
Calendar and Its History., by E. G.
Richards . . . . . . . . . . . . . . . . 92--99
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 100--102
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Thomas R. Hagedorn Notes: a Proof of a Conjecture on
Egyptian Fractions . . . . . . . . . . . ??
Peter Malcomson and
Frank Okoh Notes: Rings Without Maximal Ideals . . ??
John P. Pratt \em Mapping Time: The Calendar and Its
History, by E. G. Richards . . . . . . . ??
Alexander Russell Notes: An Easy Reduction of an
Isoperimetric Inequality on the Sphere
to Extremal Set Theory . . . . . . . . . ??
Maria Suzuki Notes: Alternative Formulations of the
Twin Prime Problem . . . . . . . . . . . ??
Jerzy Tsyzkiewicz Notes: a Simple Construction for
Tournaments With Every $k$ Players
Beaten by a Single Player . . . . . . . ??
James A. Donaldson and
Richard J. Fleming Elbert F. Cox: An Early Pioneer . . . . 105--128
Bennett Eisenberg and
Rosemary Sullivan Crofton's Differential Equation . . . . 129--139
Allen J. Schwenk What is the Correct Way to Seed a
Knockout Tournament? . . . . . . . . . . 140--150
Ali Enayat $ \delta $ as a Continuous Function of
$x$ and $ \epsilon $ . . . . . . . . . . 151--155
Frank R. Pfaff A Commutative Multiplication of Number
Triplets . . . . . . . . . . . . . . . . 156--162
Carsten Thomassen The Rendezvous Number of a Symmetric
Matrix and a Compact Connected Metric
Space . . . . . . . . . . . . . . . . . 163--166
Tamas Erdelyi On the Equation a(a + d)(a + 2d)(a + 3d)
= x$^2$ . . . . . . . . . . . . . . . . 166--169
Gerd Herzog On Nonlinear Summability . . . . . . . . 170--171
Florian Luca The Anti-Social Fermat Number . . . . . 171--173
Anatole Beck A Fractal Example in Ordinary
Differential Equations . . . . . . . . . 174--175
Leonard Smiley Problem 10781 . . . . . . . . . . . . . 176--176
Douglas Iannucci Problem 10782 . . . . . . . . . . . . . 176--176
Wu Wei Chao Problem 10783 . . . . . . . . . . . . . 176--176
Alberto Facchini and
Francesco Barioli Problem 10784 . . . . . . . . . . . . . 176--176
Emeric Deutsch Problem 10785 . . . . . . . . . . . . . 176--176
Leroy Quet Problem 10786 . . . . . . . . . . . . . 177--177
Juan Arias-de-Reyna Problem 10787 . . . . . . . . . . . . . 177--177
Warren Koepp and
Robin Chapman and
J. H. Lindsey II and
NSA Problems Group On the Intersection of Z$^n$ with a
Hyperplane: 10639 . . . . . . . . . . . 177--177
Michael A. Filaseta and
Allen Stenger and
D. Callan and
Z. Franco When a Multiple of $ \pi / 2 $ is Close
to an Integer: 10640 . . . . . . . . . . 177--179
J. Gross and
G. Trenkler and
S.-O. Troschke and
William F. Trench and
D. Callan and
G. Wahba and
R. J. Chapman and
L. M. DeAlba and
J. H. Lindsey II and
IUTS Problems Group A Property of Some Normal Matrices:
10645 . . . . . . . . . . . . . . . . . 179--180
Marcin Mazur and
Kit Hanes and
J. Anglesio and
M. Benedicty and
S. B. Ekhad and
N. Lakshmanan and
A. Nijenhuis and
J. H. Smith Tangent Lines and Collinear Points:
10673 . . . . . . . . . . . . . . . . . 180--181
Wu Wei Chao and
Michael Reid and
F. Bellot Rosado and
R. J. Chapman and
D. Donini and
S. B. Ekhad and
N. Lakshmanan and
O. P. Lossers and
A. Nijenhuis and
P. E. Nuesch and
C. G. Petalas Incenters and Excenters: 10693 . . . . . 182--184
Gerald Heuer and
Kenneth F. Andersen and
P. Fitzsimmons and
K. Heuer and
S. S. Kim and
J. H. Lindsey II and
O. P. Lossers and
K. Poelladennou and
K. Schiling and
L. Scribani and
P. Simeonov and
GCHQ Problems Group and
NSA Problems Group A Square Game: 10696 . . . . . . . . . . 184--184
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Anatole Beck Notes: a Fractal Example in Ordinary
Differential Equations . . . . . . . . . ??
Ali Enayat As a Continuous Function of $x$ and
\ldots . . . . . . . . . . . . . . . . . ??
Tamas Erdélyi Notes: On the Equation $ a (a + d)(a + 2
d)(a + 3 d) = x2 $ . . . . . . . . . . . ??
Gerd Herzog Notes: On Nonlinear Summability . . . . ??
Florian Luca Notes: The Anti-Social Fermat Number . . ??
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . ??
Francis Edward Su Book Review: \booktitleCake-Cutting
Algorithms: Be Fair If You Can, by Jack
Robertson and William Webb . . . . . . . 185--188
Carsten Thomassen Notes: The Rendezvous Number of a
Symmetric Matrix and a Compact Connected
Metric Space . . . . . . . . . . . . . . ??
Andrew M. Gleason Yueh-Gin Gung and Dr. Charles Y. Hu
Award for Distinguished Service to Paul
R. Halmos . . . . . . . . . . . . . . . 193--194
Chris Freiling and
Robert Hunter and
Cynthia Turner and
Russell C. Wheeler Tiling with Squares and Anti-Squares . . 195--204
Luis Verde-Star Solving Linear Differential-like
Equations . . . . . . . . . . . . . . . 205--218
Garry Helzer Special Relativity with Acceleration . . 219--237
Bjorn Poonen and
Fernando Rodriguez-Villegas Lattice Polygons and the Number $ 12 $ 238--250
Tom Sibley and
Stan Wagon Rhombic Penrose Tilings Can be
$3$-Colored . . . . . . . . . . . . . . 251--253
Ming-Chang Kang Cubic Fields and Radical Extensions . . 254--256
Lee Badger Generating the Measures of $n$-Balls . . 256--258
Omar Hijab The Volume of the Unit Ball in C$^n$ . . 259--259
Michael D. Hirschhorn Partial Fractions and Four Classical
Theorems of Number Theory . . . . . . . 260--264
Sung S. Kim and
Kil H. Kwon Smooth $ (C^\infty) $ but Nowhere
Analytic Functions . . . . . . . . . . . 264--266
Detlef Laugwitz Comments on the Paper ``Two Letters by
N. N. Luzin to M. Ya. Vygodskii'' . . . 267--276
Howard M. Taylor Problem 10788 . . . . . . . . . . . . . 277--277
Robin Chapman Problem 10789 . . . . . . . . . . . . . 277--277
Jean Anglesio Problem 10790 . . . . . . . . . . . . . 277--277
Antal Fekete Problem 10791 . . . . . . . . . . . . . 277--277
Harold G. Diamond and
Ferrell S. Wheeler Problem 10792 . . . . . . . . . . . . . 278--278
Florian Luca Problem 10793 . . . . . . . . . . . . . 278--278
David S. Hough and
Rodica E. Simion Problem 10794 . . . . . . . . . . . . . 278--278
David Callan and
Knut Dale and
Ivar Skau and
John Henry Steelman and
GCHQ Problem Solving Group and
J. C. Binz and
R. J. Chapman and
F. Herzig and
A. Kundgen and
R. Martin and
J. H. Nieto and
O. A. Saleh and
S. Byrd and
E. Schmeichel and
I. Sofair and
M. Vowe An Identity Involving Derangements:
10643 . . . . . . . . . . . . . . . . . 278--279
Emeric Deutsch and
John H. Lindsey II and
Michael H. Andreoli and
R. A. Agnew and
R. J. Chapman and
M. P. Cohen and
M. N. Deshpande and
M. D. Ernst and
E. Hertz and
L. R. Ivory and
W. Janous and
G. Keselman and
R. G. Mosier and
J. H. Nieto and
R. Pinkham and
S. D. Sarti and
P. Simeonov and
W. R. Smythe and
A. Stadler and
J. H. Steelman and
W. F. Trench and
J. T. Ward and
M. Woltermann and
Anchorage Math Solutions Group and
GCHQ Problems Group How Far Does the First Element
Dominate?: 10649 . . . . . . . . . . . . 279--280
David Callan and
Robin Chapman and
J. H. Lindsey II and
J. Parkinson and
V. Schindler and
P. Simeonov and
GCHQ Problems Group Analysis of a French Inheritance Law:
10652 . . . . . . . . . . . . . . . . . 280--281
Mihaly Bencze and
Dan Saracino and
Allen Stenger and
S. Amghibech and
J. Anglesio and
R. Bauer and
A. Siegel and
D. M. Bloom and
G. L. Body and
D. Callan and
R. J. Chapman and
K. Ford and
S. M. Gagola and
N. Gauthier and
W. V. Grounds and
T. Hagedorn and
R. T. Koether and
N. Komanda and
R. N. Krishnan and
K.-W. Lau and
J. H. Lindsey II and
L. E. Mattics and
C. A. Minh and
H. N. Ozsoylev and
C. Y. Yildirim and
P. G. Poonacha and
N. R. Sanjeev and
C. Popescu and
J. Robertson and
H. -J. Sieffert and
J. O. Shallit and
N. C. Singer and
A. Stadler and
D. C. Terr and
T. V. Triff and
T. Trimble and
P. Trojovsky and
Anchorage Math Solutions Group and
GCHQ Problems Group and
NSA Problems Group A Recurrence Generating Multiples of
Primes: 10655 . . . . . . . . . . . . . 281--282
James C. Owings, Jr. and
Jeremy E. Dawson and
Robin J. Chapman and
Darryl K. Nester and
R. A. Agnew and
J. Beebee and
D. Callan and
R. Garcia-Pelayo and
V. Hernandez and
J. Martin and
J. Hickman and
D. Jones and
S. S. Kim and
O. Krafft and
M. Schaefer and
G. Letac and
J. H. Lindsey II and
O. P. Lossers and
K. Poelladennou and
K. Schilling and
M. Shemesh and
GCHQ Problems Group and
NSA Problems Group A Sum of Chebyshev Inequalities: 10687 282--283
Hassan Ali Shah Ali and
John H. Lindsey II and
GCHQ Problems Group and
NSA Problems Group Extrema for Constrained Elementary
Symmetric Functions: 10694 . . . . . . . 283--283
Jose L. Diaz and
Tewodros Amdeberhan and
Erik I. Verriest A Rational Identity: 10697 . . . . . . . 283--284
Abram Kagan and
Colin Mallows and
Larry Shepp and
John H. Lindsey II Bernoulli Component of a Sum: 10699 . . 284--284
Jean Anglesio and
Shalosh B. Ekhad Four More Distinguished Points of a
Triangle: 10703 . . . . . . . . . . . . 285--285
Gerald B. Folland Book Review: \booktitle[untitled] . . . 286--291
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 292--294
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Lee Badger Notes: Generating the Measures of
$n$-Balls . . . . . . . . . . . . . . . ??
Harold P. Boas \em Graphica 1. The Imaginary Made Real:
The Images of Michael Trott; \em
Graphica 2. The Pattern of Beauty: The
Art of Igor Bakshee . . . . . . . . . . ??
Omar Hijab Notes: The Volume of the Unit Ball in $
{C}^n $ . . . . . . . . . . . . . . . . ??
Michael D. Hirschhorn Notes: Partial Fractions and Four
Classical Theorems of Number Theory . . ??
Ming-chang Kang Notes: Cubic Fields and Radical
Extensions . . . . . . . . . . . . . . . ??
Tom Sibley and
Stan Wagon Notes: Rhombic Penrose Tilings Can Be
$3$-Colored . . . . . . . . . . . . . . ??
Michael C. Sullivan Knot Factoring . . . . . . . . . . . . . 297--315
Robert S. Strichartz Evaluating Integrals Using
Self-Similarity . . . . . . . . . . . . 316--326
Joel L. Weiner How Helical Can a Closed, Twisted Space
Curve be? . . . . . . . . . . . . . . . 327--333
Chi-Kwong Li Norms, Isometries, and Isometry Groups 334--340
Francesc Aguilo and
Miguel Angel Fiol and
Maria Lluisa Fiol Periodic Tilings as a Dissection Method 341--352
Rajendra Bhatia and
Chandler Davis A Better Bound on the Variance . . . . . 353--357
J. N. Ridley An Elementary Proof on Location of Zeros 357--360
Neil Calkin and
Herbert S. Wilf Recounting the Rationals . . . . . . . . 360--363
Stephen E. Wright A Note on Positively Spanning Sets . . . 364--366
Emeric Deutsch Problem 10795 . . . . . . . . . . . . . 367--367
Floor van Lamoen Problem 10796 . . . . . . . . . . . . . 367--367
Paul Bateman and
Jeffrey Kalb Problem 10797 . . . . . . . . . . . . . 367--367
Edward Neuman Problem 10798 . . . . . . . . . . . . . 367--367
Curtis Herink and
Gary Gruenhage Problem 10799 . . . . . . . . . . . . . 367--367
Douglas Iannucci Problem 10800 . . . . . . . . . . . . . 368--368
Paul R. Pudaite and
Glen Ellyn Problem 10801 . . . . . . . . . . . . . 368--368
Richard P. Stanley and
Richard Ehrenborg and
Stephen Gagola and
R. J. Chapman and
J. H. Lindsey II Pairs with Equal Squares: 10654 . . . . 368--368
Emeric Deutsch and
David Callan and
M. Beck and
D. Beckwith and
W. Bohm and
R. F. McCoart and
GCHQ Problems Group Another Type of Lattice Path: 10658 . . 368--370
Erwin Just and
A. Berele and
J. Bergen and
K. A. Kearnes and
G. Marks and
G. P. Wene A Sufficient Condition for
Commutativity: 10661 . . . . . . . . . . 370--370
Emeric Deutsch and
Harris Kwong and
Cecil C. Rousseau and
Paul K. Stockmeyer A Formula for the Pell Sequence: 10663 370--371
Zoltan Sasvari and
Jerrold W. Grossman and
Sung Soo Kim Avoiding Uncountably Many Subsets: 10667 371--372
John Isbell and
Stephen Schanuel and
Stephen M. Gagola, Jr. and
Mowaffaq Hajja Fixed Points of Iterated Cyclic
Difference Operators: 10676 . . . . . . 372--373
Clark Kimberling and
Peter Yff and
Vasile Mihai Another Set of Concurrent Cevians: 10678 373--373
James G. Propp and
Keith A. Kearnes An Application of Sperner's Theorem:
10679 . . . . . . . . . . . . . . . . . 374--374
Kevin Ford and
Kee-Wai Lau Asymptotics of a Recurrent Sequence:
10682 . . . . . . . . . . . . . . . . . 374--375
D. W. Brown and
John Cobb A Countable Hausdorff Space with the
Fixed Point Property: 10705 . . . . . . 375--376
Zoltan Sasvari and
John H. Lindsey II An Estimate for the Normal Distribution:
10709 . . . . . . . . . . . . . . . . . 376--377
David P. Bellamy and
Felix Lazebnik and
Ray Redheffer Characterizing Solutions to Simple
Differential Equations: 10729 . . . . . 377--377
Julian F. Fleron Book Review: \booktitle[untitled] . . . 378--384
Thomas W. Cusick Book Review: \booktitle[untitled] . . . 384--386
Roger A. Horn Editor's Endnotes . . . . . . . . . . . 387--387
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Andrew Browder Topology in the Complex Plane . . . . . 393--401
Keith Kendig Is a 2000-Year-Old Formula Still Keeping
Some Secrets? . . . . . . . . . . . . . 402--415
Joseph B. Keller Optimal Running Strategy to Escape from
Pursuers . . . . . . . . . . . . . . . . 416--421
Michael Frame and
Brenda Johnson and
Jim Sauerberg Fixed Points and Fermat: a Dynamical
Systems Approach to Number Theory . . . 422--428
Laurent Bartholdi Lamps, Factorizations, and Finite Fields 429--436
Raymond T. Boute Zeroless Positional Number
Representation and String Ordering . . . 437--444
Kevin Broughan and
Nan Zhu An Integer Programming Problem with a
Linear Programming Solution . . . . . . 444--446
Terence Jackson A Short Proof That Every Prime $ p
\equiv 3 \pmod 8 $ Is of the Form $ x^2
+ 2 y^2 $ . . . . . . . . . . . . . . . 447--447
Jean-Paul Allouche and
Michel Cosnard The Komornik--Loreti Constant Is
Transcendental . . . . . . . . . . . . . 448--449
Liu Wen A Nowhere Differentiable Continuous
Function . . . . . . . . . . . . . . . . 450--453
Jacques Tits and
John Stillwell Symmetry . . . . . . . . . . . . . . . . 454--461
Doru Caragea and
Viviana Ene Problem 10802 . . . . . . . . . . . . . 462--462
Stephen Penrice Problem 10803 . . . . . . . . . . . . . 462--462
Achilleas Sinefakopoulos Problem 10804 . . . . . . . . . . . . . 462--462
Antal Fekete Problem 10805 . . . . . . . . . . . . . 462--462
Hassan Ali Shah Ali Problem 10806 . . . . . . . . . . . . . 462--462
Marc Deléglise Problem 10807 . . . . . . . . . . . . . 463--463
Enrico Valdinoci Problem 10808 . . . . . . . . . . . . . 463--463
Paul Deiermann and
Rick Mabry and
Alain Tissier Intersecting Curves: 10712 . . . . . . . 463--464
Juan-Bosco Romero Marquez and
Heinz-Jurgen Seiffert A Cute Characterization of Acute
Triangles: 10713 . . . . . . . . . . . . 464--464
Roger Cuculi\`ere and
Albert Stadler Successful Bootstrapping: 10715 . . . . 465--466
Marcin Mazur and
Robin Chapman and
Petr Lison\vek and
Robert B. Israel and
Murray S. Klamkin Rigid and Very Rigid Tetrahedra: 10717 466--467
Daniel A. Sidney and
National Security Agency Problems Group Integrals and Sines: 10721 . . . . . . . 468--469
Donald Knuth and
Darin Stephenson The Probability of Being in a State:
10726 . . . . . . . . . . . . . . . . . 469--470
Walther Janous and
Enrico Valdinoci The Best Constant in an Inequality:
10730 . . . . . . . . . . . . . . . . . 470--470
Allen C. Hibbard Book Review: \booktitle[untitled] . . . 471--474
Mic Jackson Book Review: \booktitle[untitled] . . . 474--478
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 479--481
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Edward R. Scheinerman When Close Enough is Close Enough . . . 489--499
K. Robin McLean Loops of Regular Polygons . . . . . . . 500--510
Arthur T. Benjamin and
Gregory M. Levin and
Karl Mahlburg and
Jennifer J. Quinn Random Approaches to Fibonacci
Identities . . . . . . . . . . . . . . . 511--516
D. Borwein and
J. M. Borwein and
P. Marechal Surprise Maximization . . . . . . . . . 517--527
Pei Yuan Wu Polygons and Numerical Ranges . . . . . 528--540
Pavel Pudlak Proofs as Games . . . . . . . . . . . . 541--550
Wlodzimierz Kuperberg Holey Coronas A Solution of the
Grunbaum--Shephard Conjecture on Convex
Isohedral Tilings . . . . . . . . . . . 551--555
Dan Romik Stirling's Approximation for $ n! $: The
Ultimate Short Proof? . . . . . . . . . 556--557
Richard Ehrenborg The Hankel Determinant of Exponential
Polynomials . . . . . . . . . . . . . . 557--560
Arthur T. Benjamin and
Matthew T. Fluet What's Best? . . . . . . . . . . . . . . 560--562
Doug Engel A Celtic Magnecurve Problem . . . . . . 563--565
David Beckwith Problem 10809 . . . . . . . . . . . . . 566--566
Juan-Bosco Romero Marquez Problem 10810 . . . . . . . . . . . . . 566--566
Phil Tracy Problem 10811 . . . . . . . . . . . . . 566--566
Yehuda Pinchover and
Simeon Reich Problem 10812 . . . . . . . . . . . . . 566--566
Fred Richman Problem 10813 . . . . . . . . . . . . . 567--567
Razvan Satnoianu Problem 10814 . . . . . . . . . . . . . 567--567
Barbara S. Bertram and
Otto G. Ruehr Problem 10815 . . . . . . . . . . . . . 567--567
Emeric Deutsch and
Ira M. Gessel and
David Callan Permutation Parameters with the Same
Distribution: 10634 . . . . . . . . . . 567--568
David Beckwith and
Tiberiu V. Trif and
Dan C. Popescu A Series Involving Numbers of
Factorizations: 10669 . . . . . . . . . 568--569
David Newman A Recurrence inside a Generating
Function: 10681 . . . . . . . . . . . . 569--570
Western Maryland College Problems Group A Western Maryland Integral: 10708 . . . 570--572
Bogdan Suceava and
Achilleas Sinefakopoulos A Six Point Circle: 10710 . . . . . . . 572--573
Sung Soo Kim and
K. P. Hart Partitioning the Interval into Closed
Sets: 10733 . . . . . . . . . . . . . . 573--573
David Aldous Book Review: \booktitle[untitled] . . . 574--576
Michael Frame Book Review: \booktitle[untitled] . . . 576--580
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Charles S. ReVelle and
Kenneth E. Rosing Defendens Imperium Romanum: a Classical
Problem in Military Strategy . . . . . . 585--594
Bruce C. Berndt and
Robert A. Rankin The Books Studied by Ramanujan in India 595--601
Rajendra Bhatia Pinching, Trimming, Truncating, and
Averaging of Matrices . . . . . . . . . 602--608
Gerald Beer When is a Family of Sets a Family of
Bounded Sets? . . . . . . . . . . . . . 609--614
David S. Moore and
George W. Cobb Statistics and Mathematics: Tension and
Cooperation . . . . . . . . . . . . . . 615--630
Jonathan Pakianathan and
Krishnan Shankar Nilpotent Numbers . . . . . . . . . . . 631--634
Tom Jenkyns and
Eric Muller Triangular Triples from Ceilings to
Floors . . . . . . . . . . . . . . . . . 634--639
Rodney Nillsen Normal Numbers without Measure Theory 639--644
M. M. Postnikov and
Abe Shenitzer The Problem of Squarable Lunes . . . . . 645--651
Emeric Deutsch Problem 10816 . . . . . . . . . . . . . 652--652
Walther Janous Problem 10817 . . . . . . . . . . . . . 652--652
Cezar Joita Problem 10818 . . . . . . . . . . . . . 652--652
Olaf Krafft Problem 10819 . . . . . . . . . . . . . 652--652
M. Mirzavaziri Problem 10820 . . . . . . . . . . . . . 652--652
Gerard J. Foschini Problem 10821 . . . . . . . . . . . . . 653--653
Jeffrey Lagarias Problem 10822 . . . . . . . . . . . . . 653--653
Jerrold R. Griggs and
Darryl K. Nester and
Sung Soo Kim The Asymptotics of the Birthday Problem:
10665 . . . . . . . . . . . . . . . . . 653--654
Marius Cavachi A Powerful Property: 10674 . . . . . . . 654--654
Harm Derksen and
Jeremy Dawson A Characterization of Min or Max: 10677 654--655
C. R. Pranesachar Equicevian Points of a Triangle: 10686 656--657
Wu Wei Chao and
Plamen Simeonov When Quadrilaterals Have Inscribed
Circles: 10698 . . . . . . . . . . . . . 657--658
Floor van Lamoen and
J. C. Binz Beyond the De Longchamps Point: 10734 658--659
Radu Theodorescu and
Jonathan M. Borwein Moments of the Poisson Distribution:
10738 . . . . . . . . . . . . . . . . . 659--659
Stepan Tersian and
Richard Bagby A Definite Integral: 10746 . . . . . . . 659--660
Colm Mulcahy Book Review: \booktitle[untitled] . . . 661--663
Jerrold W. Grossman Book Review: \booktitle[untitled] . . . 664--668
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 669--671
Anonymous Lester R. Ford Awards for 1999 . . . . . 672--672
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Steven L. Lee and
Gilbert Strang Row Reduction of a Matrix and A = CaB 681--688
S. Allen Broughton Constructing Kaleidoscopic Tiling
Polygons in the Hyperbolic Plane . . . . 689--710
Daniel K. Biss A Generalized Approach to the
Fundamental Group . . . . . . . . . . . 711--720
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixtieth William Lowell Putnam
Mathematical Competition . . . . . . . . 721--732
Joseph A. Gallian Putnam Trivia for the 90s . . . . . . . 733--735
Oleg Pikhurko On Envy-Free Cake Division . . . . . . . 736--738
Tom M. Apostol Calculating Higher Derivatives of
Inverses . . . . . . . . . . . . . . . . 738--741
Holly Carley and
Xin Li The Modulus of Polynomials with Zeros at
the Roots of Unity . . . . . . . . . . . 742--748
Vladimir Rako\vcevi\'c On the Norm of Idempotent Operators in a
Hilbert Space . . . . . . . . . . . . . 748--750
Guang Yuan Zhang A Simple Proof of a Theorem of Block and
Hart . . . . . . . . . . . . . . . . . . 751--751
George E. Andrews Problem 10823 . . . . . . . . . . . . . 752--752
Ho-joo Lee Problem 10824 . . . . . . . . . . . . . 752--752
Carl Miller Problem 10825 . . . . . . . . . . . . . 752--752
Félix Martínez-Giménez Problem 10826 . . . . . . . . . . . . . 752--752
Ulrich Abel Problem 10827 . . . . . . . . . . . . . 752--752
David Beckwith Problem 10828 . . . . . . . . . . . . . 753--753
Walther Janous Problem 10829 . . . . . . . . . . . . . 753--753
David Callan and
David Beckwith and
Anchorage Math Solutions Group Periodic Points and Forests: 10666 . . . 753--754
Harry Tamvakis and
Joseph J. Rushanan Splitting Triple Products by Sign: 10683 754--754
Donald E. Knuth and
Vaughan Pratt and
O. P. Lossers The Real Numbers, Algebraically: 10689 755--755
H. W. Lenstra and
National Security Agency Problems Group Restricting the Order of Elements in a
Group: 10684 . . . . . . . . . . . . . . 755--755
Glenn G. Chappell and
Robin Chapman Ordering the Integers Using Specified
Differences: 10692 . . . . . . . . . . . 756--756
Iliya Bluskov and
Albert Nijenhuis A Useful and Surprising Limit: 10695 . . 756--757
Oscar Ciaurri and
G. E. Bilodeau Variation on the Mean Value Theme: 10739 757--757
Athanasios Kalakos and
Michel Bataille and
David M. Wells A Differential Equation with Many
Solutions: 10747 . . . . . . . . . . . . 757--758
Gh. Costovici and
Kenneth Schilling Conditions Ensuring Convergence: 10752 758--759
Douglas Iannucci and
Brian D. Beasley A Cosine Formula: 10756 . . . . . . . . 759--759
H. Burgiel Book Review: \booktitle[untitled] . . . 760--763
Shirley B. Pomeranz Book Review: \booktitle[untitled] . . . 763--766
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
R. Bruce Mattingly Even Order Regular Magic Squares Are
Singular . . . . . . . . . . . . . . . . 777--782
Manjul Bhargava The Factorial Function and
Generalizations . . . . . . . . . . . . 783--799
Jason Jeffers Lost Theorems of Geometry . . . . . . . 800--812
Walter Rudin Sums of Squares of Polynomials . . . . . 813--821
Edward B. Burger Diophantine Olympics and World
Champions: Polynomials and Primes Down
Under . . . . . . . . . . . . . . . . . 822--829
Serge Tabachnikov A Four Vertex Theorem for Polygons . . . 830--833
Glyn Harman and
Kam C. Wong A Note on The Metrical Theory of
Continued Fractions . . . . . . . . . . 834--837
Peter Kravanja and
Ann Haegemans Multidimensional Analytic Deflation . . 837--841
Tom M. Apostol Irrationality of The Square Root of Two
-- A Geometric Proof . . . . . . . . . . 841--842
Anindya Sen Fundamental Theorem of Algebra -- Yet
Another Proof . . . . . . . . . . . . . 842--843
Walter Felscher Bolzano, Cauchy, Epsilon, Delta . . . . 844--862
Floor van Lamoen Problem 10830 . . . . . . . . . . . . . 863--863
George E. Andrews and
P. Paule and
A. Riese Problem 10831 . . . . . . . . . . . . . 863--863
Donald E. Knuth Problem 10832 . . . . . . . . . . . . . 863--863
Charles Vanden Eynden Problem 10833 . . . . . . . . . . . . . 863--863
Sung Soo Kim Problem 10834 . . . . . . . . . . . . . 864--864
Anna Dyubina and
Pierre de la Harpe Problem 10835 . . . . . . . . . . . . . 864--864
Jon A. Wellner Problem 10836 . . . . . . . . . . . . . 864--864
Leroy Quet and
Robin Chapman Bernoulli, Stirling, and Stirling: 10700 864--865
William G. Spohn, Jr. and
Jeremy E. Dawson Neighborly Pythagorean Triples: 10704 865--866
James G. Propp and
Tiberiu V. Trif Deriving a Perfect Square: 10706 . . . . 866--867
C\ualin Popescu and
Achilleas Sinefakopoulos Inequalities Involving Altitudes and
Exradii: 10759 . . . . . . . . . . . . . 867--868
Leroy Quet and
O. P. Lossers A Convoluted Recursion: 10762 . . . . . 868--868
Ray Redheffer and
Robin Chapman All Solutions in the Unit Cube: 10764 868--869
Szilárd András and
Ronald A. Kopas and
Heinz-Jürgen Seiffert Symmetric Inequalities for x$^x$ and
x$^{x 2}$ : 10766 . . . . . . . . . . . 869--870
Steve Kennedy Book Review: \booktitle[untitled] . . . 871--874
Marion D. Cohen Book Review: \booktitle[untitled] . . . 874--876
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 877--878
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Carolyn Eschenbach and
Frank Hall and
Rohan Hemasinha and
Stephen Kirkland and
Zhongshan Li and
Bryan Shader and
Jeffrey Stuart and
James Weaver Properties of Tournaments among
Well-Matched Players . . . . . . . . . . 881--892
M. A. Hernández Cifre Is There a Planar Convex Set with Given
Width, Diameter, and Inradius? . . . . . 893--900
John Konvalina A Unified Interpretation of the Binomial
Coefficients, the Stirling Numbers, and
the Gaussian Coefficients . . . . . . . 901--910
Stefan Treatman and
Cameron Wickham Constructible Approximations of Regular
Polygons . . . . . . . . . . . . . . . . 911--922
David M. Bradley Using Integral Transforms to Estimate
Higher Order Derivatives . . . . . . . . 923--931
Reid Barton and
Keith Burns A Simple Special Case of Sharkovskii's
Theorem . . . . . . . . . . . . . . . . 932--933
William Watkins The Quadratic Residues -1 and -3 . . . . 934--934
Gerd Herzog Polynomials Solving Dirichlet Boundary
Value Problems . . . . . . . . . . . . . 934--936
Karl Dilcher An Extension of Fermat's Little Theorem,
and Congruences for Stirling Numbers . . 936--940
Floor van Lamoen Morley Related Triangles on the
Nine-Point Circle . . . . . . . . . . . 941--945
Árpád Bényi and
Pawel Szeptycki and
Fred Van Vleck Archimedean Properties and Parabolas . . 945--949
Ho-joo Lee Problem 10837 . . . . . . . . . . . . . 950--950
Florian S. Pârvânescu Problem 10838 . . . . . . . . . . . . . 950--950
Beresford N. Parlett Problem 10839 . . . . . . . . . . . . . 950--950
Jiansheng Yang and
Shulin Zhou Problem 10840 . . . . . . . . . . . . . 950--950
Erwin Just Problem 10841 . . . . . . . . . . . . . 950--950
Bruce Reznick Problem 10842 . . . . . . . . . . . . . 950--950
Kent D. Boklan and
John P. Robertson The Maximum Length of a Powerful
Arithmetic Progression: 10702 . . . . . 951--951
Andrew Vince Problem 10843 . . . . . . . . . . . . . 951--951
John Isbell and
Julio Kuplinsky and
Leon Mattics A Union of Proper Subspaces?: 10707 . . 951--952
Jean Anglesio and
Volkhard Schindler Two Triangles with Common Vertex,
Incenter, and Centroid: 10719 . . . . . 952--954
Mowaffaq Hajja and
Peter Walker and
Danny Arrigo and
Xiaoshen Wang and
Zafar Ahmed A Cubic Spherical Integral: 10771 . . . 954--955
William C. Waterhouse and
Steve Butcher Nonconstant Functions with Derivative
Zero: 10772 . . . . . . . . . . . . . . 956--956
Zafar Ahmed and
Peter M. Jarvis A Family of Integrals: 10777 . . . . . . 956--957
Kiran Kedlaya and
Marcin Mazur Incircle Partnerships: 10780 . . . . . . 957--958
Paul Deiermann and
Rick Mabry Intersecting Curves: 10712 . . . . . . . 958--958
Marion D. Cohen Book Review: \booktitle[untitled] . . . 959--963
J. David Logan Book Review: \booktitle[untitled] . . . 964--967
Roger A. Horn Editor's Endnotes . . . . . . . . . . . 968--969
Anonymous Volume Information . . . . . . . . . . . 970--980
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
W. E. Kirwan Mathematics Departments in the 21st
Century: Role, Relevance, and
Responsibility . . . . . . . . . . . . . 1--9
David Garber and
Boaz Tsaban A Mechanical Derivation of the Area of
the Sphere . . . . . . . . . . . . . . . 10--15
David J. Aldous Reorganizing Large Web Sites . . . . . . 16--27
Dean Alvis and
Michael Kinyon Birkhoff's Theorem for Panstochastic
Matrices . . . . . . . . . . . . . . . . 28--37
Chaim Goodman-Strauss Compass and Straightedge in the Poincaré
Disk . . . . . . . . . . . . . . . . . . 38--49
Eric Schechter Constructivism Is Difficult . . . . . . 50--54
Ira M. Gessel The Smith College Diploma Problem . . . 55--57
William C. Waterhouse Cochran's Theorem for Rings . . . . . . 58--59
Andrew Simoson The Tumbling Tetrahedron . . . . . . . . 59--63
David Eppstein Tangent Spheres and Triangle Centers . . 63--66
Marc Noy Acyclic and Totally Cyclic Orientations
in Planar Graphs . . . . . . . . . . . . 66--68
Takayuki Furuta The Hölder--McCarthy and the Young
Inequalities Are Equivalent for Hilbert
Space Operators . . . . . . . . . . . . 68--69
John Stillwell Modular Miracles . . . . . . . . . . . . 70--76
Nick MacKinnon Problem 10844 . . . . . . . . . . . . . 77--77
Ciprian Demeter Problem 10845 . . . . . . . . . . . . . 77--77
Józef Przytycki Problem 10846 . . . . . . . . . . . . . 77--77
Robin Chapman and
Kimmo Eriksson and
Richard Stanley Problem 10847 . . . . . . . . . . . . . 77--77
Kenneth B. Stolarsky Problem 10848 . . . . . . . . . . . . . 77--77
Richard Bagby Problem 10849 . . . . . . . . . . . . . 78--78
Wolfdieter Lang Problem 10850 . . . . . . . . . . . . . 78--78
David M. Bradley and
Steven Levandosky and
A. Meir Series and Integral Trial Conditions:
10642 . . . . . . . . . . . . . . . . . 78--79
Fred Galvin and
Stephen C. Locke and
Sung Soo Kim and
David Callan A Generalization of Hall's Theorem:
10701 . . . . . . . . . . . . . . . . . 79--80
Florian Luca and
Francis B. Coghlan Can Two Consecutive Numbers Both Be
Perfect?: 10711 . . . . . . . . . . . . 80--81
Jet Wimp and
Thomas Hermann A Determinant with Polynomial Entries:
10714 . . . . . . . . . . . . . . . . . 81--81
Michael L. Catalano-Johnson and
Daniel Loeb and
John Beebee A Cubical Gift: 10716 . . . . . . . . . 81--82
Sung Soo Kim and
Mark D. Meyerson When a Sum of Functions Is Increasing:
10768 . . . . . . . . . . . . . . . . . 82--82
Wu Wei Chao and
Daniele Donini Concurrent Lines in a Cyclic
Quadrilateral: 10783 . . . . . . . . . . 83--83
Leroy Quet and
Reiner Martin and
Otto G. Ruehr A Zeta Function Series: 10786 . . . . . 84--84
Doron Zeilberger Book Review: \booktitle[untitled] . . . 85--86
John Guckenheimer Book Review: \booktitle[untitled] . . . 87--89
William G. McCallum Book Review: \booktitleCalculus
Mysteries and Thrillers, by R. Grant
Woods; How to Ace Calculus: The
Streetwise Guide ~by Colin Adams; Joel
Hass; Abigail Thompson . . . . . . . . . 90--93
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 94--96
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Henry L. Alder Yueh-Gin Gung and Dr. Charles Y. Hu
Award to Manuel P. Berriozábal for
Distinguished Service to Mathematics . . 97--99
Duane DeTemple and
Matthew Hudelson Square-Banded Polygons and Affine
Regularity . . . . . . . . . . . . . . . 100--114
Peter D. Lax Change of Variables in Multiple
Integrals II . . . . . . . . . . . . . . 115--119
Adam Korányi Around the Finite-Dimensional Spectral
Theorem . . . . . . . . . . . . . . . . 120--125
William Mueller Reform Now, before It's Too Late! . . . 126--143
H. Turgay Kaptano\uglu In Praise of $ y = x^\alpha \sin (1 / x)
$ . . . . . . . . . . . . . . . . . . . 144--150
Jean B. Lasserre and
Konstantin E. Avrachenkov The Multi-Dimensional Version of $
\int^b_a x^p \, d x $ . . . . . . . . . 151--154
Sibylle Zeller and
Maximilian Thaler Almost Sure Escape from the Unit
Interval under the Logistic Map . . . . 155--158
Robert Geretschläger and
Walther Janous Generalized Rearrangement Inequalities 158--165
Seannie Dar and
Shay Gueron A Weighted Erd\Hos--Mordell Inequality 165--168
Jan J. Dijkstra A Four-Point Set That Cannot Be Split 168--170
David Beckwith Problem 10851 . . . . . . . . . . . . . 171--171
C\ualin Popescu Problem 10852 . . . . . . . . . . . . . 171--171
Stevo Stevi\'c Problem 10853 . . . . . . . . . . . . . 171--171
Wu Wei Chao Problem 10854 . . . . . . . . . . . . . 171--171
Ernesto Bruno Cossi Problem 10855 . . . . . . . . . . . . . 171--171
Andrei Jorza Problem 10856 . . . . . . . . . . . . . 172--172
Harold G. Diamond Problem 10857 . . . . . . . . . . . . . 172--172
Emeric Deutsch and
Murray S. Klamkin and
Denis Constales Counting the Solutions: 10540 . . . . . 172--173
David M. Bloom and
Stephen M. Gagola, Jr. Dirichlet Knew It All along: 10718 . . . 174--174
Richard F. McCoart and
Lyle Ramshaw More Balls in Urns: 10722 . . . . . . . 174--176
Christopher J. Hillar and
Heinz-Jürgen Seiffert Two Sums That Are Congruent Modulo p:
10723 . . . . . . . . . . . . . . . . . 176--176
Andrei Jorza and
O. P. Lossers Maximum of a Polynomial on the Unit
Circle: 10779 . . . . . . . . . . . . . 177--177
Antal Fekete and
Gary Martin Squared Series Yielding Integers: 10791 177--178
Edward Newman and
Li Zhou A Mean Inequality: 10798 . . . . . . . . 178--178
Robert A. Fontenot Book Review: \booktitle[untitled] . . . 179--182
Doris Schattschneider Book Review: \booktitle[untitled] . . . 182--188
Ben Herbst Book Review: \booktitle[untitled] . . . 188--190
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Frank Morgan Proof of the Double Bubble Conjecture 193--205
Paul R. Wolfson The Crooked Made Straight: Roberval and
Newton on Tangents . . . . . . . . . . . 206--216
David Spring Solution of a Calculus Problem on
Minimal Volume . . . . . . . . . . . . . 217--221
Dirk Huylebrouck Similarities in Irrationality Proofs for
$ \pi $, $ \ln 2 $, $ \zeta (2) $, and $
\zeta (3) $ . . . . . . . . . . . . . . 222--231
Lidia Aceto and
Donato Trigiante The Matrices of Pascal and Other Greats 232--245
Graham Byrnes and
Grant Cairns and
Barry Jessup Leftovers from the Ham Sandwich Theorem 246--249
Patrick Martinez Some New Irrational Decimal Fractions 250--253
Pantelis A. Damianou Monic Polynomials in Z[x] with Roots in
the Unit Disc . . . . . . . . . . . . . 253--257
Egon Scheffold Pythagorean Triples of Polygonal Numbers 257--258
Hans J. H. Tuenter A Symmetry of Power Sum Polynomials and
Bernoulli Numbers . . . . . . . . . . . 258--261
Paul Yiu Heronian Triangles Are Lattice Triangles 261--263
Vl. P. Vizgin On the Emotional Assumptions without
Which One Could Not Effectively
Investigate the Laws of Nature . . . . . 264--270
Donald E. Knuth Problem 10858 . . . . . . . . . . . . . 271--271
Roland Bacher Problem 10859 . . . . . . . . . . . . . 271--271
Emeric Deutsch Problem 10860 . . . . . . . . . . . . . 271--271
Sung Soo Kim Problem 10861 . . . . . . . . . . . . . 271--271
Wu Wei Chao Problem 10862 . . . . . . . . . . . . . 271--271
Leroy Quet Problem 10863 . . . . . . . . . . . . . 272--272
C\ualin Popescu Problem 10864 . . . . . . . . . . . . . 272--272
Vasile Mihai and
Michael Woltermann The Smoothest and Roughest Permutations:
10725 . . . . . . . . . . . . . . . . . 272--273
Jean Anglesio and
O. P. Lossers Periods from Sums of Powers: 10727 . . . 273--273
M. N. Deshpande and
John H. Lindsey II The Total Length of Short Cycles of a
Random Permutation: 10732 . . . . . . . 273--274
Hassan Ali Shah Ali and
National Security Agency Problems Group Getting the Same Weighted Average Two
Ways: 10737 . . . . . . . . . . . . . . 274--274
Tim Keller and
Javier Cilleruelo Squares with Four Equal Digits in an
Even Base: 10741 . . . . . . . . . . . . 275--275
Juan Arias-de-Reyna and
Robin Chapman The Square of a Random Determinant:
10787 . . . . . . . . . . . . . . . . . 275--277
Harold G. Diamond and
Ferrell S. Wheeler A Convolution Formula for the Dickman
Function: 10792 . . . . . . . . . . . . 277--278
Curtis Herink and
Gary Gruenhage and
GCHQ Problems Group Finite Subcovers for Open Covers with
Exact Cardinality: 10799 . . . . . . . . 278--278
Susan G. Staples Book Review: \booktitle[untitled] . . . 279--280
George E. Andrews Book Review: \booktitle[untitled] . . . 281--285
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 286--288
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Rajendra Bhatia Linear Algebra to Quantum Cohomology:
The Story of Alfred Horn's Inequalities 289--318
R. Shail A Proof of Thébault's Theorem . . . . . . 319--325
John H. Hubbard and
Samer S. Habre and
Beverly H. West The Convergence of an Euler
Approximation of an Initial Value
Problem Is Not Always Obvious . . . . . 326--335
Garret Sobczyk The Missing Spectral Basis in Algebra
and Number Theory . . . . . . . . . . . 336--346
Rachel W. Hall and
Kre\vsimir Josi\'c The Mathematics of Musical Instruments 347--357
Holger Schellwat A Simple Slide Rule for Finite Fields 358--360
Razvan Alin Satnoianu A General Method for Establishing
Geometric Inequalities in a Triangle . . 360--364
J. M. Aldaz and
A. Bravo and
S. Gutiérrez and
A. Ubis A Theorem of D. J. Newman on Euler's $
\phi $ Function and Arithmetic
Progressions . . . . . . . . . . . . . . 364--367
Liu Wen A Counterexample for the Two-Dimensional
Density Function . . . . . . . . . . . . 367--368
N. S. Astapov and
N. C. Noland The Remarkable Tetron . . . . . . . . . 368--370
David Beckwith Problem 10865 . . . . . . . . . . . . . 371--371
Jerry Kazdan and
Herbert Wilf Problem 10866 . . . . . . . . . . . . . 371--371
Oscar Ciaurri Ramirez Problem 10867 . . . . . . . . . . . . . 371--371
M. N. Deshpande and
A. V. Kharashikar Problem 10868 . . . . . . . . . . . . . 371--371
Lenny Jones Problem 10869 . . . . . . . . . . . . . 372--372
Hugh L. Montgomery and
Ulrike M. A. Vorhauer Problem 10870 . . . . . . . . . . . . . 372--372
Donald E. Knuth Problem 10871 . . . . . . . . . . . . . 372--372
Titu Andreescu and
Gilbert N. Lewis Preserving the Sum of Three Cubes: 10728 372--373
Gustavus J. Simmons and
John Henry Steelman and
GCHQ Problem Solving Group and
O. P. Lossers A Congruence for Pascal Triangular
Matrices: 10735 . . . . . . . . . . . . 373--374
Mizan R. Khan An Optimization with a Modular
Constraint: 10736 . . . . . . . . . . . 374--375
Charles Vanden Eynden and
Jerrold W. Grossman Distinguishing between the Partite Sets
of a Bipartite Graph: 10740 . . . . . . 375--375
Emre Alkan and
Stephen Gagola, Jr. The Maximal Property for Finite Groups:
10742 . . . . . . . . . . . . . . . . . 375--376
C\ualin Popescu and
O. P. Lossers Comparing a Sum over Quadratic Residues
and Nonresidues: 10743 . . . . . . . . . 376--377
Jiro Fukuta Not Quite a Theorem on Quadrilaterals:
10755 . . . . . . . . . . . . . . . . . 377--378
Achilleas Sinefakopoulos and
Daniele Donini Cirumscribing an Inscribed
Quadrilateral: 10804 . . . . . . . . . . 378--378
Arthur M. Hobbs Book Review: \booktitle[untitled] . . . 379--381
Eli Maor Book Review: \booktitle[untitled] . . . 382--385
Harsh V. Pittie Book Review: \booktitle[untitled] . . . 386--387
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Constance Reid The Alternative Life of E. T. Bell . . . 393--402
Peter Lindqvist and
Jaak Peetre Two Remarkable Identities, Called Twos,
for Inverses to Some Abelian Integrals 403--410
Judy Kennedy and
Sahin Koçak and
James A. Yorke A Chaos Lemma . . . . . . . . . . . . . 411--423
Robert E. Greene Real Analyticity: From Calculus Class to
the Grauert--Morrey Theorem . . . . . . 424--431
Erik Talvila Some Divergent Trigonometric Integrals 432--436
Fred Brauer What Goes Up Must Come Down, Eventually 437--440
Edsger W. Dijkstra and
Jayadev Misra Designing a Calculational Proof of
Cantor's Theorem . . . . . . . . . . . . 440--443
Giuseppe De Marco For Every $ \epsilon $ There
Continuously Exists a $ \delta $ . . . . 443--444
Antreas P. Hatzipolakis and
Paul Yiu The Lucas Circles of a Triangle . . . . 444--446
Gerald B. Folland How to Integrate a Polynomial over a
Sphere . . . . . . . . . . . . . . . . . 446--448
V. Wiktor Marek and
Jan Mycielski Foundations of Mathematics in the
Twentieth Century . . . . . . . . . . . 449--468
Bogdan Suceav\ua Problem 10872 . . . . . . . . . . . . . 469--469
B. J. Venkatachala Problem 10873 . . . . . . . . . . . . . 469--469
Wu Wei Chao Problem 10874 . . . . . . . . . . . . . 469--469
Donald E. Knuth Problem 10875 . . . . . . . . . . . . . 469--469
Zoltán Sasvári Problem 10876 . . . . . . . . . . . . . 469--469
Emeric Deutsch Problem 10877 . . . . . . . . . . . . . 470--470
Pál Péter Dályay Problem 10878 . . . . . . . . . . . . . 470--470
S. C. Locke and
Phil Tracy and
H.-J. Voss Highly Cohesive Graphs Have Long
Nonseparating Paths: 10647 . . . . . . . 470--472
Serge Tabachnikov Polyhedron Covered Twice by Lines: 10724 472--473
Peter Lindqvist and
Jaak Peetre and
Jonathan M. Borwein Generalized Trigonometric Functions:
10744 . . . . . . . . . . . . . . . . . 473--474
Marc Deléglise and
Joe Flowers An Unusual Limit Problem: 10807 . . . . 474--475
Yehuda Pinchover and
Simeon Reich and
Itai Shafrir The Ptolemy Constant of a Normed Space:
10812 . . . . . . . . . . . . . . . . . 475--476
Yves Nievergelt Book Review: \booktitle[untitled] . . . 477--481
David Scott Book Review: \booktitle[untitled] . . . 481--485
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 486--487
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Paul C. Pasles The Lost Squares of Dr. Franklin: Ben
Franklin's Missing Squares and the
Secret of the Magic Circle . . . . . . . 489--511
Martin Hanke and
Otmar Scherzer Inverse Problems Light: Numerical
Differentiation . . . . . . . . . . . . 512--521
Hans Samelson Differential Forms, the Early Days; or
the Stories of Deahna's Theorem and of
Volterra's Theorem . . . . . . . . . . . 522--530
C. J. Maxson and
J. H. Meyer How Many Subspaces Force Linearity? . . 531--536
Wim Pijls Some Properties Related to Mercator
Projection . . . . . . . . . . . . . . . 537--543
Erik Talvila Necessary and Sufficient Conditions for
Differentiating under the Integral Sign 544--548
Jean-P. Quadrat and
Jean B. Lasserre and
Jean-B. Hiriart-Urruty Pythagoras' Theorem for Areas . . . . . 549--551
David A. Sánchez An Alternative to the Shooting Method
for a Certain Class of Boundary Value
Problems . . . . . . . . . . . . . . . . 552--555
Wen-jin Woan Uniform Partitions of Lattice Paths and
Chung--Feller Generalizations . . . . . 556--559
Harley Flanders From Ford to Fa\`a . . . . . . . . . . . 559--561
Mowaffaq Hajja A Vector Proof of a Theorem of Bang . . 562--564
Walther Janous Problem 10879 . . . . . . . . . . . . . 565--565
Razvan A. Satnoianu Problem 10880 . . . . . . . . . . . . . 565--565
José Luis Palacios Problem 10881 . . . . . . . . . . . . . 565--565
Erwin Just and
Norman Schaumberger Problem 10882 . . . . . . . . . . . . . 565--565
Nick MacKinnon Problem 10883 . . . . . . . . . . . . . 565--565
Zafar Ahmed Problem 10884 . . . . . . . . . . . . . 566--566
Kiran Kedlaya and
Sasha Schwartz Problem 10885 . . . . . . . . . . . . . 566--566
M. J. Pelling and
GCHQ Problem Solving Group Maximizing Quadratic Forms over Cubes:
10731 . . . . . . . . . . . . . . . . . 566--567
Alain Grigis and
W. Weston Meyer Reflections of a Billiard Path: 10749 567--567
Jean Anglesio and
Con Amore Problems Group A Nowhere-Differentiable Function from
Geometry: 10790 . . . . . . . . . . . . 568--568
Floor van Lamoen and
W. Weston Meyer Euler Lines Concurrent on the Nine-Point
Circle: 10796 . . . . . . . . . . . . . 569--569
Hassan Ali Shah Ali and
Keith A. Kearnes and
Ágnes Szenderei and
Zafar Ahmed and
M. A. Prasad and
GCHQ Problems Group A Difference of Square Roots: 10806 . . 570--570
Juan-Bosco Romero Marquez and
Mohammed Ali Salem A Parallelogram Inscribed in a
Quadrilateral: 10810 . . . . . . . . . . 571--571
Razvan Satnoianu and
Li Zhou Relatives of Erd\Hos--Mordell: 10814 . . 572--572
Marion D. Cohen Book Review: \booktitle[untitled] . . . 573--577
J. Alan Alewine and
Eric Schechter Book Review: \booktitle[untitled] . . . 577--582
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Jeffrey R. Weeks The Twin Paradox in a Closed Universe 585--590
Chi-Kwong Li and
Stephen Pierce Linear Preserver Problems . . . . . . . 591--605
David E. Zitarelli Towering Figures in American
Mathematics, 1890-1950 . . . . . . . . . 606--635
Erik Talvila Rapidly Growing Fourier Integrals . . . 636--641
Soren Boel and
Toke Meier Carlsen and
Niels Richard Hansen A Useful Strengthening of the
Stone--Weierstrass Theorem . . . . . . . 642--643
Xingzhi Zhan Linear Preservers That Permute the
Entries of a Matrix . . . . . . . . . . 643--645
Darrell Desbrow A Real Antiderivative by Contour
Integration . . . . . . . . . . . . . . 645--649
Vesa Halava and
Tero Harju Mortality in Matrix Semigroups . . . . . 649--653
Michael Atiyah Mathematics in the 20th Century . . . . 654--666
Joaquín Gómez Rey Problem 10886 . . . . . . . . . . . . . 667--667
Jean Anglesio Problem 10887 . . . . . . . . . . . . . 667--667
William P. Wardlaw and
William D. Withers Problem 10888 . . . . . . . . . . . . . 667--667
Klaus Huber Problem 10889 . . . . . . . . . . . . . 667--667
Raymond Mortini Problem 10890 . . . . . . . . . . . . . 668--668
Roland Bacher Problem 10891 . . . . . . . . . . . . . 668--668
Stephen C. Locke Problem 10892 . . . . . . . . . . . . . 668--668
M. J. Pelling and
F. W. Roush The Sum Divides the Product: 10745 . . . 668--669
Itshak Borosh and
Douglas A. Hensley and
Joel Zinn and
GCHQ Problem Solving Group One Good Congruence Deserves Another:
10748 . . . . . . . . . . . . . . . . . 669--669
Leonard Smiley and
David Callan and
David M. Wells and
Said Amghibech A Rational Generating Function for
Relative Divisors: 10750 . . . . . . . . 670--670
Jean Anglesio and
Daniele Donini Special Points of the Triangle of
Excenters: 10763 . . . . . . . . . . . . 671--671
Barbara S. Bertram and
Otto G. Ruehr Submultiplicativity of a Function
Defined by a Series: 10815 . . . . . . . 671--672
Frank Swetz Book Review: \booktitle[untitled] . . . 673--675
Eli Maor Book Review: \booktitle[untitled] . . . 675--677
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 678--680
Anonymous Lester R. Ford Awards for 2000 . . . . . 681--681
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
David Lindsay Roberts E. H. Moore's Early Twentieth-Century
Program for Reform in Mathematics
Education . . . . . . . . . . . . . . . 689--696
Shaun M. Fallat Bidiagonal Factorizations of Totally
Nonnegative Matrices . . . . . . . . . . 697--712
Don Rawlings Sequential Searches: Proofreading,
Russian Roulette, and the Incomplete
$q$-Eulerian Polynomials Revisited . . . 713--720
Jan E. Holly Pictures of Ultrametric Spaces, the
$p$-Adic Numbers, and Valued Fields . . 721--728
Kenneth R. Meyer Jacobi Elliptic Functions from a
Dynamical Systems Point of View . . . . 729--737
P. J. McKenna and
Cillian Ó Tuama Large Torsional Oscillations in
Suspension Bridges Visited Again:
Vertical Forcing Creates Torsional
Response . . . . . . . . . . . . . . . . 738--745
Greg Martin Absolutely Abnormal Numbers . . . . . . 746--754
Christopher Stuart Limiting Distributions for Derangements 755--755
Keith McKenzie Rogers The Finite Field Kakeya Problem . . . . 756--759
Airton von Sohsten de Medeiros The Fundamental Theorem of Algebra
Revisited . . . . . . . . . . . . . . . 759--760
Mowaffaq Hajja Other Versions of the Steiner--Lehmus
Theorem . . . . . . . . . . . . . . . . 760--767
Wladimir de Azevedo Pribitkin A Simpler Proof of $ s i n \pi z = \pi z
\prod_{k = 1}^\infty (1 - z^2 / k^2) $ 767--768
Jean B. Lasserre A Quick Proof for the Volume of
$n$-Balls . . . . . . . . . . . . . . . 768--769
Andrei Jorza Problem 10893 . . . . . . . . . . . . . 770--770
Robert Sulanke Problem 10894 . . . . . . . . . . . . . 770--770
A\=ug\=ust Wendijk Problem 10895 . . . . . . . . . . . . . 770--770
Torben Maack Bisgaard and
Zsolt Páles and
Zoltan Sasvari Problem 10896 . . . . . . . . . . . . . 770--770
Gregory P. Wene Problem 10897 . . . . . . . . . . . . . 771--771
Wu Wei Chao Problem 10898 . . . . . . . . . . . . . 771--771
R. Martini and
G. F. Post Problem 10899 . . . . . . . . . . . . . 771--771
Paul Bracken and
Bruce S. Burdick Euler's Formula for Zeta Function
Convolutions: 10754 . . . . . . . . . . 771--773
Bruce Reznick and
Bruce Dearden Completely Multiplicative Functions:
10760 . . . . . . . . . . . . . . . . . 773--773
Fred Galvin and
Radhika Ramamurthi An Extremal Problem for Independent Sets
in Graphs: 10761 . . . . . . . . . . . . 773--774
Bruce Dearden and
Jerry Metzer and
Robert Gilmer Invertible Matrices Modulo n: 10767 . . 774--774
Christian Blatter and
Josh Greene The Chromatic Number of the Sphere:
10769 . . . . . . . . . . . . . . . . . 774--775
Enrico Valdinoci and
Robin Chapman Convergence of a Series: 10808 . . . . . 775--777
Walther Janous and
Anne-Maria Ernvall A Summation Inequality: 10817 . . . . . 777--777
O. A. Laudal Book Review: \booktitle[untitled] . . . 778--781
O. Carruth McGehee Book Review: \booktitle[untitled] . . . 782--784
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
William Mueller Mathematical Wunderkammern . . . . . . . 785--796
Jimmie D. Lawson and
Yongdo Lim The Geometric Mean, Matrices, Metrics,
and More . . . . . . . . . . . . . . . . 797--812
Robert Osserman Kepler's Laws, Newton's Laws, and the
Search for New Planets . . . . . . . . . 813--820
Dan Kalman and
James E. White Polynomial Equations and Circulant
Matrices . . . . . . . . . . . . . . . . 821--840
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-First William Lowell Putnam
Mathematical Competition . . . . . . . . 841--850
Ákos László The Sum of Some Convergent Series . . . 851--855
A. G. Ramm A Simple Proof of the Fredholm
Alternative and a Characterization of
the Fredholm Operators . . . . . . . . . 855--860
Robert L. Benedetto An Elementary Product Identity in
Polynomial Dynamics . . . . . . . . . . 860--864
Jeremy Gray Weierstrass, Luzin, and Intuition . . . 865--870
Gordon Rice Problem 10900 . . . . . . . . . . . . . 871--871
M. J. Knight Problem 10901 . . . . . . . . . . . . . 871--871
Emeric Deutsch Problem 10902 . . . . . . . . . . . . . 871--871
Richard Bagby Problem 10903 . . . . . . . . . . . . . 871--871
Ovidiu Furdui Problem 10904 . . . . . . . . . . . . . 871--871
Richard P. Stanley Problem 10905 . . . . . . . . . . . . . 871--871
Donald E. Knuth Problem 10906 . . . . . . . . . . . . . 872--872
Emeric Deutsch and
David Callan and
Sabin Cautis and
Southwest Missouri Problems Group Another Path to Generalized Catalan
Numbers: 10751 . . . . . . . . . . . . . 872--873
Louis Shapiro and
Richard Ehrenborg and
John W. Moon and
Michael Reid Leaves of Ordered Trees: 10753 . . . . . 873--874
Mark Kidwell and
Donald Knuth and
O. P. Lossers Leaves of Ordered Trees: 10757 . . . . . 874--875
Gerard J. Foschini and
GCHQ Problems Group A Sequence of Functions That Doesn't
Span L$_2$ [0,1]: 10821 . . . . . . . . 875--876
Jeffrey Lagarias and
Jade Vinson and
GCHQ Problems Group When Periodic Points Are Real: 10822 . . 876--877
Félix Martínez-Giménez and
John H. Lindsey II A Convergence Property for Infinite
Arrays: 10826 . . . . . . . . . . . . . 877--877
Donald E. Knuth and
Cecil C. Rousseau A Stirling Series: 10832 . . . . . . . . 877--878
Armand Borel Book Review: \booktitle[untitled] . . . 879--883
Mark A. Kon Book Review: \booktitle[untitled] . . . 883--887
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 888--890
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Peter Borwein and
Loki Jörgenson Visible Structures in Number Theory . . 897--910
Donald R. Chalice How to Differentiate and Integrate
Sequences . . . . . . . . . . . . . . . 911--921
David Alan Grier Dr. Veblen Takes a Uniform Mathematics
in the First World War . . . . . . . . . 922--931
Harriet Pollatsek Quantum Error Correction: Classic Group
Theory Meets a Quantum Challenge . . . . 932--962
Yunhi Cho and
Kyunghwan Park Inverse Functions of $ y = x^{1 / x} $ 963--967
Hiroshi Maehara On the Total Edge-Length of a
Tetrahedron . . . . . . . . . . . . . . 967--969
Eugenio P. Balanzario Evaluation of Dirichlet Series . . . . . 969--971
Timothy G. Feeman and
Osvaldo Marrero Affine Transformations, Polynomials, and
Proportionality . . . . . . . . . . . . 972--975
Szilárd András Problem 10907 . . . . . . . . . . . . . 976--976
Wu Wei Chao Problem 10908 . . . . . . . . . . . . . 976--976
Támás Kalmán Problem 10909 . . . . . . . . . . . . . 976--976
Stevo Stevi\'c and
Rade Todorovi\'c Problem 10910 . . . . . . . . . . . . . 976--976
Greg Martin Problem 10911 . . . . . . . . . . . . . 976--976
Jean Anglesio Problem 10912 . . . . . . . . . . . . . 976--976
Donald E. Knuth Problem 10913 . . . . . . . . . . . . . 977--977
Mark Sapir and
O. P. Lossers and
Hugh L. Montgomery The Decimal Expansions of Powers of 9:
10758 . . . . . . . . . . . . . . . . . 977--978
Peter J. Ferraro Fibonacci Numbers and Powers: 10765 . . 978--979
C\ualin Popescu and
Jim Vandergriff and
Jim Delany A Divisibility Result for a Combination
of mth Powers: 10770 . . . . . . . . . . 979--980
Emeric Deutsch and
Jim Brawner Three-Dimensional Lattice Walks in the
Upper Half-Space: 10795 . . . . . . . . 980--980
Jon A. Wellner and
M. L. Glasser Incognito Hypergeometrics: 10836 . . . . 980--981
Andrew Vince and
Kenneth Schilling Almost Fixed Sets: 10843 . . . . . . . . 981--982
Fred Galvin A Generalization of Hall's Theorem:
10701 . . . . . . . . . . . . . . . . . 982--982
Neal Koblitz Book Review: \booktitle[untitled] . . . 983--988
Anthony Ralston Book Review: \booktitle[untitled] . . . 988--992
Roger A. Horn Editor's Endnotes . . . . . . . . . . . 993--994
Anonymous Volume Information . . . . . . . . . . . 995--1006
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Robert Almgren Financial Derivatives and Partial
Differential Equations . . . . . . . . . 1--12
Richard Evan Schwartz Lucy and Lily: a Game of Geometry and
Number Theory . . . . . . . . . . . . . 13--20
J. A. C. Weideman Numerical Integration of Periodic
Functions: a Few Examples . . . . . . . 21--36
Victor L. Shapiro Harmonic Functions in the Unit Disk . . 37--45
Sérgio B. Volchan What Is a Random Sequence? . . . . . . . 46--63
Paolo Roselli and
Michel Willem A Convexity Inequality . . . . . . . . . 64--70
William C. Waterhouse Quadratic Polynomials and Unique
Factorization . . . . . . . . . . . . . 70--72
C. Ballantine and
J. Roberts A Simple Proof of Rolle's Theorem for
Finite Fields . . . . . . . . . . . . . 72--74
Thomas Sellke Yet Another Proof of the Radon--Nikodým
Theorem . . . . . . . . . . . . . . . . 74--76
Giovanni Falcone Problem 10914 . . . . . . . . . . . . . 77--77
C. P. Rupert Problem 10915 . . . . . . . . . . . . . 77--77
Gertrude Ehrlich Problem 10916 . . . . . . . . . . . . . 77--77
Jürgen Groß and
Götz Trenkler Problem 10917 . . . . . . . . . . . . . 77--77
Matthias Beck Problem 10918 . . . . . . . . . . . . . 77--77
Michael Becker Problem 10919 . . . . . . . . . . . . . 77--78
André Kündgen and
Radhika Ramamurthi Problem 10920 . . . . . . . . . . . . . 78--78
Nick MacKinnon and
Stephen M. Gagola, Jr. Fibonacci Twin Primes: 10844 . . . . . . 78--78
Ciprian Demeter and
Li Zhou Another Collinearity Result for
Triangles: 10845 . . . . . . . . . . . . 78--79
Józef Przytycki and
Richard Stong Shrinking Lattice Curves: 10846 . . . . 79--80
Robin Chapman and
Kimmo Ericksson and
Richard P. Stanley and
Reiner Martin On the Number of Divisors of $n$ in a
Special Interval: 10847 . . . . . . . . 80--80
Kenneth Stolarsky and
NSA Problems Group and
O. P. Lossers A Characterization of a Quadratic
Polynomial: 10848 . . . . . . . . . . . 80--81
Richard Bagby and
M. Battaile The Determinant of a Matrix of Sines:
10849 . . . . . . . . . . . . . . . . . 81--82
Wolfdieter Lang and
Said Amghibech On a Matrix Obtained from the Catalan
Generating Function: 10850 . . . . . . . 82--83
D. S. Mitrinovi\'c and
Slavko Simic Special Functions from Long Ago: 5626 83--84
Stan Wagon Book Review: \booktitle[untitled] . . . 85--92
Duncan Buell Book Review: \booktitle[untitled] . . . 93--98
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 99--101
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 102--102
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Eleanor Robson Words and Pictures: New Light on
Plimpton 322 . . . . . . . . . . . . . . 105--120
Audrey Terras Finite Quantum Chaos . . . . . . . . . . 121--139
Aaron Abrams and
Robert Ghrist Finding Topology in a Factory:
Configuration Spaces . . . . . . . . . . 140--150
Arthur Baragar Constructions Using a Compass and
Twice-Notched Straightedge . . . . . . . 151--164
Frank Morgan and
Roger Bolton Hexagonal Economic Regions Solve the
Location Problem . . . . . . . . . . . . 165--172
James Kuzmanovich and
Andrey Pavlichenkov Finite Groups of Matrices Whose Entries
Are Integers . . . . . . . . . . . . . . 173--186
Liu Zheng An Elementary Proof for Two Basic
Alternating Series . . . . . . . . . . . 187--188
Robert A. Agnew On the TEAM Approach to Investing . . . 188--192
Craig Huneke The Friendship Theorem . . . . . . . . . 192--194
Claude-Alain Faure A Short Proof of Lebesgue's Density
Theorem . . . . . . . . . . . . . . . . 194--196
Josef Hofbauer A Simple Proof of $ 1 + (1 / 2)^2 + (1 /
3)^2 + \cdots {} = \pi^2 / 6 $ and
Related Identities . . . . . . . . . . . 196--200
David M. Bloom Problem 10921 . . . . . . . . . . . . . 201--201
Mizan R. Khan Problem 10922 . . . . . . . . . . . . . 201--201
Stephen B. Gray Problem 10923 . . . . . . . . . . . . . 201--201
A. J. Sasane Problem 10924 . . . . . . . . . . . . . 201--201
David Callan Problem 10925 . . . . . . . . . . . . . 201--202
Harold Diamond Problem 10926 . . . . . . . . . . . . . 202--202
Jeffrey C. Lagarias and
E. M. Rains and
N. J. A. Sloane Problem 10927 . . . . . . . . . . . . . 202--202
Jean Anglesio and
Reiner Martin Continued Fractions for Some Quadratic
Surds: 10773 . . . . . . . . . . . . . . 202--203
Catalin Zara and
Zachary Franco and
T. S. Michael and
Todor E. Milev A High-Powered Fibonacci Identity: 10774 203--204
Paul Bateman and
Dennis Eichhorn and
Robin Chapman Grouping $k$-Tuples of Integers by the
Sum of Their Squares: 10778 . . . . . . 204--205
Robin Chapman and
M. A. Prasad An Expression for Even-Indexed Bernoulli
Numbers: 10789 . . . . . . . . . . . . . 205--206
Florian Luca and
Nasha Komanda A Number and Its Totient Are Not
Amicable: 10793 . . . . . . . . . . . . 206--207
David S. Hough and
Rodica E. Simion and
Ali Ekber Gürel Divisors of Generalized Catalan Numbers:
10794 . . . . . . . . . . . . . . . . . 207--208
C\ualin Popescu and
Roy Barbara and
Omran Kouba A Sum Related to Quadratic Residues:
10852 . . . . . . . . . . . . . . . . . 208--208
Gail Ratcliff Book Review: \booktitle[untitled] . . . 209--211
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Warren P. Johnson The Curious History of Fa\`a di Bruno's
Formula . . . . . . . . . . . . . . . . 217--234
Wladimir de Azevedo Pribitkin Laplace's Integral, the Gamma Function,
and beyond . . . . . . . . . . . . . . . 235--245
Sam Northshield Associativity of the Secant Method . . . 246--257
Aimee S. A. Johnson and
Kathleen Madden Renewal Systems, Sharp-Eyed Snakes, and
Shifts of Finite Type . . . . . . . . . 258--272
Warren P. Johnson Combinatorics of Higher Derivatives of
Inverses . . . . . . . . . . . . . . . . 273--277
Christian Radoux The Hankel Determinant of Exponential
Polynomials: a Very Short Proof and a
New Result Concerning Euler Numbers . . 277--278
Karl Dilcher and
Kurt Girstmair Dedekind Sums and Uniform Distributions 279--284
Robbert Fokkink R$^3$ Has No Root . . . . . . . . . . . 285--285
John Stillwell The Continuum Problem . . . . . . . . . 286--297
Christopher J. Hillar Problem 10928 . . . . . . . . . . . . . 298--298
Lajos Csete Problem 10929 . . . . . . . . . . . . . 298--298
Paul Schweitzer Problem 10930 . . . . . . . . . . . . . 298--298
Robert DiSario Problem 10931 . . . . . . . . . . . . . 298--298
Christian Bey and
Jerrold R. Griggs Problem 10932 . . . . . . . . . . . . . 298--299
Paul Lescott Problem 10933 . . . . . . . . . . . . . 299--299
Vasile Mihai Problem 10934 . . . . . . . . . . . . . 299--299
Hadi Salmasian and
NSA Problems Group Minimizing the Sum of Negative Powers of
Orders of Group Elements: 10775 . . . . 299--299
Yongge Tian and
David W. Carter Squashing a Matrix by Adding an
Imaginary Part: 10776 . . . . . . . . . 300--300
Leonard Smiley and
GCHQ Problem Solving Group and
Helmut Prodinger and
Robin Chapman A Tree-Counting Identity: 10781 . . . . 300--301
Douglas Iannucci and
O. P. Lossers and
GCHQ Problem Solving Group Divisibility Involving Random Sets of
Integers: 10782 . . . . . . . . . . . . 301--302
Emeric Deutsch and
John Henry Steelman and
David Callan A Recursively Defined Sequence of
Functions: 10785 . . . . . . . . . . . . 302--304
Douglas Iannucci and
Kee-Wai Lau Triperfect Numbers: 10800 . . . . . . . 304--305
Wu Wei Chao and
Geoffrey A. Kandall The Median Meets the Circle of
Appolonius: 10862 . . . . . . . . . . . 305--305
Judith V. Grabiner Book Review: \booktitle[untitled] . . . 306--309
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 310--312
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 313--314
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Alan D. Taylor The Manipulability of Voting Systems . . 321--337
Jeffrey C. Lagarias and
Colin L. Mallows and
Allan R. Wilks Beyond the Descartes Circle Theorem . . 338--361
Shay Gueron Two Applications of the Generalized
Ptolemy Theorem . . . . . . . . . . . . 362--370
Rita Aggarwala and
Michael P. Lamoureux Inverting the Pascal Matrix Plus One . . 371--377
Liu Wen A Nowhere Differentiable Continuous
Function Constructed by Infinite
Products . . . . . . . . . . . . . . . . 378--380
Johannes Huisman Rino's Flight around the World in
Circles . . . . . . . . . . . . . . . . 380--383
Casey Mann A Tile with Surround Number 2 . . . . . 383--388
Reinhard Michel On Stirling's Formula . . . . . . . . . 388--390
Andrea Vietri An Inductive Proof of a Known Result
about $ \psi (x) $ . . . . . . . . . . . 390--391
Zhibing Chen Problem 10935 . . . . . . . . . . . . . 392--392
Andor Lukács and
Szilard András Problem 10936 . . . . . . . . . . . . . 392--392
David G. Wagner Problem 10937 . . . . . . . . . . . . . 392--392
Jean-Pierre Grivaux Problem 10938 . . . . . . . . . . . . . 392--392
Aleksandar Ivic Problem 10939 . . . . . . . . . . . . . 392--392
Yves Nievergelt Problem 10940 . . . . . . . . . . . . . 393--393
Jeffrey C. Lagarias Problem 10941 . . . . . . . . . . . . . 393--393
Paul Bateman and
Jeffrey Kalb and
Allen Stenger A Limit Involving Least Common
Multiples: 10797 . . . . . . . . . . . . 393--394
Paul R. Pudaite and
Owen Byer and
Deirdre Smeltzer A Gambler Urns His Money: 10801 . . . . 394--395
Stephen Penrice and
GCHQ Problem Solving Group Expected Rank in an NBA Draft Lottery:
10803 . . . . . . . . . . . . . . . . . 395--396
Floor van Lamoen Circumcenters on a Circle: 10830 . . . . 396--397
Florian S. Pârvânescu and
Roy Barbara When ABC Is Equilateral: 10838 . . . . . 397--398
Jiansheng Yang and
Shulin Zhou and
O. P. Lossers An Elaborate Uniform Convergence: 10840 398--399
J. David Logan Book Review: \booktitle[untitled] . . . 400--402
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Jason Cantarella and
Dennis DeTurck and
Herman Gluck Vector Calculus and the Topology of
Domains in $3$-Space . . . . . . . . . . 409--442
Shay Gueron and
Ran Tessler The Fermat--Steiner Problem . . . . . . 443--451
M. Ram Murty Prime Numbers and Irreducible
Polynomials . . . . . . . . . . . . . . 452--458
Alf van der Poorten and
Gerhard Woeginger Squares from Products of Consecutive
Integers . . . . . . . . . . . . . . . . 459--462
Jeff Brooks and
Satha Push The Cycloidal Pendulum . . . . . . . . . 463--465
Paulo Viana and
Paula Murgel Veloso Galois Theory of Reciprocal Polynomials 466--471
Mira Bhargava When Is a Group the Union of Proper
Normal Subgroups? . . . . . . . . . . . 471--473
Gregory F. Bachelis A Short Proof of Hall's Theorem on SDRs 473--474
Walther Janous Problem 10942 . . . . . . . . . . . . . 475--475
C\ualin Popescu Problem 10943 . . . . . . . . . . . . . 475--475
Marcin Mazur Problem 10944 . . . . . . . . . . . . . 475--475
Slavko Simic Problem 10945 . . . . . . . . . . . . . 475--476
Stevo Stevi\'c Problem 10946 . . . . . . . . . . . . . 476--476
LSU Problem Solving Group Problem 10947 . . . . . . . . . . . . . 476--476
Peter Walker Problem 10948 . . . . . . . . . . . . . 476--476
Antal Fekete and
Johann Cigler Stirling and Bell and Binomial, Oh My!:
10805 . . . . . . . . . . . . . . . . . 476--477
David Beckwith and
Karl David An Identity for Partitions of Integers:
10809 . . . . . . . . . . . . . . . . . 477--478
Phil Tracy and
NCCU Problems Group The Distance between the Endpoints of a
Longest Path: 10811 . . . . . . . . . . 478--478
Emeric Deutsch and
Wen-jin Woan Special Motzkin Paths: 10816 . . . . . . 478--479
Cezar Joita and
Robin Chapman The Functional Equation $ f \circ g = f
$: 10818 . . . . . . . . . . . . . . . . 479--480
Olaf Krafft and
Gabriela St\uanic\ua and
Pantelimon St\uanic\ua A Binomial Coefficient Estimate: 10819 480--481
Ho-joo Lee and
Marc A. P. Bernstein Brocard Angle 30 Degrees: 10824 . . . . 481--482
Ulrich Abel and
Douglas B. Tyler Reminiscent of Gibbs: 10827 . . . . . . 482--482
Marion D. Cohen Book Review: \booktitle[untitled] . . . 483--485
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 486--488
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Elena Anne Marchisotto The Theorem of Pappus: a Bridge between
Algebra and Geometry . . . . . . . . . . 497--516
Carrie E. Finch and
Lenny Jones A Curious Connection between Fermat
Numbers and Finite Groups . . . . . . . 517--524
Tom M. Apostol and
Mamikon A. Mnatsakanian Subtangents -- An Aid to Visual Calculus 525--533
Jeffrey C. Lagarias An Elementary Problem Equivalent to the
Riemann Hypothesis . . . . . . . . . . . 534--543
Leonard Gillman Two Classical Surprises Concerning the
Axiom of Choice and the Continuum
Hypothesis . . . . . . . . . . . . . . . 544--553
G. E. Hardy and
M. V. Subbarao A Modified Problem of Pillai and Some
Related Questions . . . . . . . . . . . 554--559
M. A. Nyblom Some Curious Sequences Involving Floor
and Ceiling Functions . . . . . . . . . 559--564
Timothy G. Feeman and
Osvaldo Marrero The Right-Hand Derivative of an Integral 565--568
Jeffrey Lagarias Problem 10949 . . . . . . . . . . . . . 569--569
Ovidiu Furdui Problem 10950 . . . . . . . . . . . . . 569--569
Sung Soo Kim Problem 10951 . . . . . . . . . . . . . 569--569
David Callan Problem 10952 . . . . . . . . . . . . . 569--569
Leroy Quet Problem 10953 . . . . . . . . . . . . . 570--570
Erwin Just and
Norman Schaumberger Problem 10954 . . . . . . . . . . . . . 570--570
Razvan Satnoianu Problem 10955 . . . . . . . . . . . . . 570--570
Doru Caragea and
Viviana Ene and
Dean Alvis and
Nasha Komanda A Millennial Polynomial Problem: 10802 570--571
Fred Richman and
NCCU Problems Group Subspaces of the Vector Space of
$2$-by-$2$ Matrices: 10813 . . . . . . . 571--572
Stevo Stevi\'c and
Alain Tissier The Limit of a Sequence: 10853 . . . . . 572--573
Harold Diamond and
Alain Tissier Truncated Series Ratios Alternating
about tanh x: 10857 . . . . . . . . . . 573--574
C\ualin Popescu and
Xiaoshen Wang and
Thomas McMillan Compact Subsets Countable: 10864 . . . . 574--574
Oscar Ciaurri Ramirez and
Daniele Donini Sum of an Infinite Series: 10867 . . . . 575--576
Claude LeBrun Book Review: \booktitle[untitled] . . . 577--578
George H. Swift Book Review: \booktitle[untitled] . . . 579--580
Anonymous [untitled] . . . . . . . . . . . . . . . 581--583
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Bob Witte The 2001 James R. C. Leitzel Lecture:
What I Have Learned from the Mathematics
Community . . . . . . . . . . . . . . . 585--594
Robert F. Brown and
Jack E. Girolo Isolating Fixed Points . . . . . . . . . 595--611
James T. Smith Thomsen's Equation . . . . . . . . . . . 612--622
John McCleary Trigonometries . . . . . . . . . . . . . 623--638
Ezra Brown and
Bruce T. Myers Elliptic Curves from Mordell to
Diophantus and Back . . . . . . . . . . 639--649
Robert L. Lamphere Solution of the Direct Problem of
Uniform Circular Motion in Non-Euclidean
Geometry . . . . . . . . . . . . . . . . 650--655
M. J. Jamieson Fibonacci Numbers and Cotangent
Sequences . . . . . . . . . . . . . . . 655--657
Iosif Pinelis An Equidistribution Phenomenon: Is There
a Principle behind It? . . . . . . . . . 657--659
P. G. Walsh On a Question of Kaplansky . . . . . . . 660--661
Judy A. Holdener A Theorem of Touchard on the Form of Odd
Perfect Numbers . . . . . . . . . . . . 661--663
John McCarthy Problem 10956 . . . . . . . . . . . . . 664--664
Victor Alexandrov Problem 10957 . . . . . . . . . . . . . 664--664
Robin Chapman Problem 10958 . . . . . . . . . . . . . 664--664
George L. Lamb Problem 10959 . . . . . . . . . . . . . 665--665
Oliver Eng Problem 10960 . . . . . . . . . . . . . 665--665
Brian Conrad Problem 10961 . . . . . . . . . . . . . 665--665
Mih\`aly Bencze Problem 10962 . . . . . . . . . . . . . 665--665
Alberto Facchini and
Francesco Barioli and
Robin Chapman and
Ron Martin Carroll Nonsingular Sums of Matrices: 10784 . . 665--666
George E. Andrews and
Robin Chapman and
George Andrews A Sparse Determinant: 10831 . . . . . . 666--667
Sung Soo Kim and
Richard Johnsonbaugh and
Ronald E. Prather and
Donald Knuth Min-Plus Matrix Multiplication: 10834 667--668
Ernesto Bruno Cossi and
Robin Chapman Points on a Sphere: 10855 . . . . . . . 668--669
Jerry Kazdan and
Herbert Wilf and
Darryl K. Nester Waiting for the Bus: 10866 . . . . . . . 669--669
Wu Wei Chao and
Li Zhou Parallelogram Circumcenters: 10874 . . . 669--670
Erwin Just and
Norman Schaumberger and
Paul Budney A Little Convexity: 10882 . . . . . . . 670--670
Zafar Ahmed and
Knut Dale and
George L. Lamb Jr. Definitely an Integral: 10884 . . . . . 670--671
Jeffrey Nunemacher Book Review: \booktitle[untitled] . . . 672--675
Mark Green Book Review: \booktitle[untitled] . . . 675--678
Anonymous Telegraphic Reviews . . . . . . . . . . 679--681
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Scott Bailey and
Theodore Kim and
Robert S. Strichartz Inside the Lévy Dragon . . . . . . . . . 689--703
Anthony Philippakis The Orthic Triangle and the O.K.
Quadrilateral . . . . . . . . . . . . . 704--728
F. Rodriguez Villegas and
L. Sadun and
J. F. Voloch Blet: a Mathematical Puzzle . . . . . . 729--740
Mark Levene and
George Loizou Kemeny's Constant and the Random Surfer 741--745
Daniel J. Velleman Partial Fractions, Binomial
Coefficients, and the Integral of an Odd
Power of $ \sec \theta $ . . . . . . . . 746--749
Per E. Manne and
Steven R. Finch A Solution to the Bent Wire Problem . . 750--752
B. Liseo A Probabilistic Derivation of Dirichlet
Integrals . . . . . . . . . . . . . . . 753--754
Roberto Sánchez-Peregrino A Note on a Closed Formula for
Poly-Bernoulli Numbers . . . . . . . . . 755--756
Harold R. Parks and
Dean C. Wills An Elementary Calculation of the
Dihedral Angle of the Regular
$n$-Simplex . . . . . . . . . . . . . . 756--758
Paul Deiermann Problem 10963 . . . . . . . . . . . . . 759--759
H. A. ShahAli Problem 10964 . . . . . . . . . . . . . 759--759
John Melville Problem 10965 . . . . . . . . . . . . . 759--759
Jean-Marie de Koninck Problem 10966 . . . . . . . . . . . . . 759--759
Douglas B. West Problem 10967 . . . . . . . . . . . . . 759--759
Stephen C. Locke Problem 10968 . . . . . . . . . . . . . 759--760
Richard Stanley Problem 10969 . . . . . . . . . . . . . 760--760
Ovidiu Furdui Problem 10950 . . . . . . . . . . . . . 760--760
M. Mirzavaziri and
GCHQ Problems Group Least Number with Exactly $m$ Divisors:
10820 . . . . . . . . . . . . . . . . . 760--761
George E. Andrews and
Karl David and
S. J. Bernau and
M. Getz and
D. Jones Periodicity under Shift and Complement:
10823 . . . . . . . . . . . . . . . . . 761--762
Carl Miller and
Donald E. Knuth A Fibonacci--Lucas Extremum: 10825 . . . 762--763
Walther Janous and
Rolf Richberg and
Raul A. Simon A Totient Sum: 10829 . . . . . . . . . . 763--763
Sung Soo Kim and
Richard Johnsonbaugh and
Ronald E. Prather and
Donald Knuth Min-Plus Matrix Multiplication: 10834 763--764
Razvan A. Satnoianu and
O. P. Lossers The Minimum Median: 10880 . . . . . . . 764--765
Klaus Huber and
O. P. Lossers and
Norbert Ortner and
A. Serret Cassini's Length: 10889 . . . . . . . . 765--766
Arthur M. Hobbs Book Review: \booktitle[untitled] . . . 767--770
Robert G. Bartle Book Review: \booktitle[untitled] . . . 770--773
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 774--776
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Ulrich Daepp and
Pamela Gorkin and
Raymond Mortini Ellipses and Finite Blaschke Products 785--795
Daniel C. Isaksen A Cohomological Viewpoint on Elementary
School Arithmetic . . . . . . . . . . . 796--805
Bennett Eisenberg and
Rosemary Sullivan The Fundamental Theorem of Calculus in
Two Dimensions . . . . . . . . . . . . . 806--817
Iwan Praton Cutting Polyominos into Equal-Area
Triangles . . . . . . . . . . . . . . . 818--826
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-Second William Lowell Putnam
Mathematical Competition . . . . . . . . 827--839
Chun-Hung Hsu and
Ming-Chia Li Transitivity Implies Period Six: a
Simple Proof . . . . . . . . . . . . . . 840--843
N. J. Wildberger A New Proof of Cavalieri's Quadrature
Formula . . . . . . . . . . . . . . . . 843--845
Li Yingying On Euler's Constant-Calculating Sums by
Integrals . . . . . . . . . . . . . . . 845--850
Alf van der Poorten Life on the Edge . . . . . . . . . . . . 850--853
Razvan Satnoianu Problem 10970 . . . . . . . . . . . . . 854--854
C. P. Rupert Problem 10971 . . . . . . . . . . . . . 854--854
Tim Ferguson and
Lenny Jones Problem 10972 . . . . . . . . . . . . . 854--854
L. D. Servi Problem 10973 . . . . . . . . . . . . . 854--854
Syrous Marivani Problem 10974 . . . . . . . . . . . . . 854--855
Emeric Deutsch Problem 10975 . . . . . . . . . . . . . 855--855
Vitaly Voloshin Problem 10976 . . . . . . . . . . . . . 855--855
Howard M. Taylor and
Richard A. Groeneveld and
John Stufken and
J. G. Kemeny and
J. L. Snell and
A. W. Knapp A Careless Walk toward Zero: 10788 . . . 855--856
David Beckwith and
NCCU Problems Group Additive Atoms: 10828 . . . . . . . . . 856--857
Anna Dyubina and
Stephen M. Gagola Jr. A Group That Is Not Finitely Generated:
10835 . . . . . . . . . . . . . . . . . 857--858
Erwin Just and
Charles Lanski Consequences of a Relation on a Ring:
10841 . . . . . . . . . . . . . . . . . 858--858
Bruce Reznick and
GCHQ Problems Group and
Li Zhou Nondivisibility of Binomial
Coefficients: 10842 . . . . . . . . . . 858--859
David Beckwith and
Li Zhou and
David Callan A Property of the Binary Sum of a Family
of Sets: 10865 . . . . . . . . . . . . . 859--860
R. Martini and
G. F. Post and
Gerald Leibowitz An Inequality of Hardy: 10899 . . . . . 860--860
Ovidio Furdui and
Albert Nijenhuis A Square Property: 10904 . . . . . . . . 860--861
Fred Richman Book Review: \booktitle[untitled] . . . 862--865
Anonymous Telegraphic Reviews . . . . . . . . . . 866--868
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Amy Shell-Gellasch Mina Rees and the Funding of the
Mathematical Sciences . . . . . . . . . 873--889
Mark Levi Minimal Perimeter Triangles . . . . . . 890--899
Tom M. Apostol and
Mamikon A. Mnatsakanian Tangents and Subtangents Used to
Calculate Areas . . . . . . . . . . . . 900--908
Richard P. Jerrard and
John E. Wetzel Equilateral Triangles and Triangles . . 909--915
Manuel Benito and
J. Javier Escribano An Easy Proof of Hurwitz's Theorem . . . 916--918
Joshua E. Greene A New Short Proof of Kneser's Conjecture 918--920
Carl Axness Problem 10977 . . . . . . . . . . . . . 921--921
Jean-Pierre Grivaux Problem 10978 . . . . . . . . . . . . . 921--921
Donald P. Minassian Problem 10979 . . . . . . . . . . . . . 921--921
Ye Zhong Hao Problem 10980 . . . . . . . . . . . . . 921--921
Nicholas C. Singer Problem 10981 . . . . . . . . . . . . . 922--922
Yuming Chen Problem 10982 . . . . . . . . . . . . . 922--922
Bogdan Suceav\ua Problem 10983 . . . . . . . . . . . . . 922--922
Beresford N. Parlett and
Olaf Krafft and
Martin Schaefer The Largest Eigenvalue of a Positive
Definite Symmetric Matrix: 10839 . . . . 922--923
Sung Soo Kim and
Charles Diminnie and
Roger Zarnowski Intermediate Value Functions: 10861 . . 923--923
Szilárd András and
Michael Reid Arithmetic Means and Geometric Means:
10907 . . . . . . . . . . . . . . . . . 924--925
Wu Wei Chao and
Richard Stong and
Doyle Henderson A Functional Equation: 10908 . . . . . . 925--926
Támás Kalmán and
O. P. Lossers Isodynamic Points of a Triangle: 10909 926--927
Stevo Stevi\'c and
Rade Todorovi\'c and
Peter M. Jarvis $ n x \bmod 1 $: 10910 . . . . . . . . . 927--928
Anonymous Errata: 10948 . . . . . . . . . . . . . 928--928
Anonymous Errata: 10950 . . . . . . . . . . . . . 928--928
Anonymous Errata: 10953 . . . . . . . . . . . . . 928--928
Anonymous Errata: An Expression for Even-Indexed
Bernoulli Numbers: 10789 . . . . . . . . 928--928
Anonymous Errata: Squashing a Matrix by Adding an
Imaginary Part: 10776 . . . . . . . . . 928--928
Anonymous Errata: Triperfect Numbers: 10800 . . . 928--928
Marion Cohen Book Review: \booktitle[untitled] . . . 929--932
Anonymous Volume Information . . . . . . . . . . . 933--943
Anonymous Back Matter . . . . . . . . . . . . . . 944--945
Anonymous Front Matter . . . . . . . . . . . . . . ??
Rüdger Thiele Hilbert's Twenty-Fourth Problem . . . . 1--24
Glenn Iba and
James Tanton Candy Sharing . . . . . . . . . . . . . 25--35
John E. McCarthy Pick's Theorem --- What's the Big Deal? 36--45
Florian Luca Fermat Primes and Heron Triangles with
Prime Power Sides . . . . . . . . . . . 46--49
Jennifer T. Betcher and
John H. Jaroma An Extension of the Results of Servais
and Cramer on Odd Perfect and Odd
Multiply Perfect Numbers . . . . . . . . 49--52
Alan Nash A Generalized Parallelogram Law . . . . 52--57
Uri Elias Rearrangement of a Conditionally
Convergent Series . . . . . . . . . . . 57--57
Yongge Tian Problem 10984 . . . . . . . . . . . . . 58--58
Donald Knuth Problem 10985 . . . . . . . . . . . . . 58--58
Herbert Wilf Problem 10986 . . . . . . . . . . . . . 58--58
Kumar N. Prasanna and
B. G. Shenoy Problem 10987 . . . . . . . . . . . . . 58--58
Wu Wei Chao Problem 10988 . . . . . . . . . . . . . 59--59
Roland Bacher Problem 10989 . . . . . . . . . . . . . 59--59
Rick Mabry Problem 10990 . . . . . . . . . . . . . 59--59
Donald E. Knuth and
Allan Pedersen Highly Variable Lists: 10691 . . . . . . 59--60
Donald E. Knuth and
O. P. Lossers Exploring All Binary Mazes: 10720 . . . 60--61
Emeric Deutsch and
Doyle Henderson and
GCHQ Problem Group Three Recurrences for a Single Sequence:
10860 . . . . . . . . . . . . . . . . . 61--62
Raymond Mortini and
Jeff Boersema Inequivalent Topologies: 10890 . . . . . 62--63
August Wendijk and
Thomas Hermann Twin Segments in the Arbelos: 10895 . . 63--64
M. J. Knight and
Li Zhou Hidden Arctangents: 10901 . . . . . . . 64--64
Michael Becker and
Rolf Richberg A Moment Evaluation: 10919 . . . . . . . 64--65
Victor Pambuccian Book Review: \booktitleGeometry: Euclid
and Beyond, by Robin Hartshorne . . . . 66--70
Della D. Fenster Book Review: \booktitle[untitled] . . . 70--74
Anonymous Telegraphic Reviews . . . . . . . . . . 75--77
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 78--80
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
R. Michael Range Complex Analysis: a Brief Tour into
Higher Dimensions . . . . . . . . . . . 89--108
Harold L. Schoen and
Christian R. Hirsch Responding to Calls for Change in High
School Mathematics: Implications for
Collegiate Mathematics . . . . . . . . . 109--123
David J. Hunter and
Paul T. von Hippel How Rare Is Symmetry in Musical $ 12
$-Tone Rows? . . . . . . . . . . . . . . 124--132
J. Peter May Munshi's Proof of the Nullstellensatz 133--140
J. M. Aldaz and
A. Bravo Euclid's Argument on the Infinitude of
Primes . . . . . . . . . . . . . . . . . 141--142
Jack B. Brown and
George Kozlowski Smooth Interpolation, Hölder Continuity,
and the Takagi--van der Waerden Function 142--147
Bang-Yen Chen When Does the Position Vector of a Space
Curve Always Lie in Its Rectifying
Plane? . . . . . . . . . . . . . . . . . 147--152
Xingzhi Zhan The Sharp Rado Theorem for Majorizations 152--153
Gabriel Navarro On the Fundamental Theorem of Finite
Abelian Groups . . . . . . . . . . . . . 153--154
Raymond Mortini Problem 10991 . . . . . . . . . . . . . 155--155
David Lubell Problem 10992 . . . . . . . . . . . . . 155--155
Giorgio Goldoni Problem 10993 . . . . . . . . . . . . . 155--155
David Savitt Problem 10994 . . . . . . . . . . . . . 155--156
Donato Trigiante Problem 10995 . . . . . . . . . . . . . 156--156
Wu Wei Chao Problem 10996 . . . . . . . . . . . . . 156--156
Ed T. Prothro Problem 10997 . . . . . . . . . . . . . 156--156
V. Thebault and
B. J. English It's a Long Story: 3887 . . . . . . . . 156--158
Charles Vanden Eynden and
Reiner Martin A Divisibility Property of Factorials:
10833 . . . . . . . . . . . . . . . . . 158--158
Ho-joo Lee and
Gerald Myerson Consecutive Integers Whose Totients Are
Multiples of n: 10837 . . . . . . . . . 158--159
Leroy Quet and
Richard Stong An Alternating Sum Involving Unsigned
Stirling Numbers: 10863 . . . . . . . . 159--160
Lenny Jones and
Florian Luca Euler to the Rescue: 10869 . . . . . . . 160--160
Hugh L. Montgomery and
John H. Lindsey II Positivity of a Certain Power Series:
10870 . . . . . . . . . . . . . . . . . 160--161
Donald E. Knuth and
Gabriel D. Carroll Balanced Neighborhood Squares: 10871 . . 161--162
Bogdan Suceav\va and
Richard Stong The Fewest $3$-Cycles to Generate an
Even Permutation: 10872 . . . . . . . . 162--162
M. Victor Wickerhauser Book Review: \booktitle[untitled] . . . 163--167
Steven G. Krantz Book Review: \booktitle[untitled] . . . 167--171
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Robert E. Megginson Yueh-Gin Gung and Dr. Charles Y. Hu
Award to Clarence F. Stephens for
Distinguished Service to Mathematics . . 177--180
Stan Gudder Quantum Computation . . . . . . . . . . 181--201
John Bamberg and
Grant Cairns and
Devin Kilminster The Crystallographic Restriction,
Permutations, and Goldbach's Conjecture 202--209
Stephen B. Gray Generalizing the Petr--Douglas--Neumann
Theorem on $N$-Gons . . . . . . . . . . 210--227
Lorenz Halbeisen Can Kirkman's Schoolgirls Walk Abreast
by Forming Arithmetic Progressions? . . 228--231
Ján Miná\vc Newton's Identities Once Again! . . . . 232--234
Michael Hardy An Illuminating Counterexample . . . . . 234--238
Ritsuo Nakamoto A Norm Inequality for Hermitian
Operators . . . . . . . . . . . . . . . 238--239
Roberto Tauraso Problem 10998 . . . . . . . . . . . . . 240--240
D. P. Minassian Problem 10999 . . . . . . . . . . . . . 240--240
George Lamb Problem 11000 . . . . . . . . . . . . . 240--240
Rick Mabry Problem 11001 . . . . . . . . . . . . . 240--240
Y.-F. S. Pétermann Problem 11002 . . . . . . . . . . . . . 240--241
Stephen B. Gray Problem 11003 . . . . . . . . . . . . . 241--241
Victor Pambuccian Problem 11004 . . . . . . . . . . . . . 241--241
M. N. Deshpande and
A. V. Kharashikar and
Walther Janous Recursive Expressions in an Urn Problem:
10868 . . . . . . . . . . . . . . . . . 241--243
B. J. Venkatachala and
Doyle Henderson An Exponential Diophantine Equation:
10873 . . . . . . . . . . . . . . . . . 243--243
Donald E. Knuth and
Richard Stong Animals in a Cage: 10875 . . . . . . . . 243--245
Emeric Deutsch and
Daniele Donini Counting Tilings with L-Tiles and
Squares: 10877 . . . . . . . . . . . . . 245--246
Walther Janous Pairs of Squares: 10879 . . . . . . . . 246--247
José Luis Palacios and
Richard Stong Going around Randomly in Circles: 10881 247--247
William Mueller Book Review: \booktitle[untitled] . . . 248--254
Shandelle M. Henson Book Review: \booktitle[untitled] . . . 254--258
Anonymous Telegraphic Reviews . . . . . . . . . . 259--261
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
George W. Cobb and
Yung-Pin Chen An Application of Markov Chain Monte
Carlo to Community Ecology . . . . . . . 265--288
Alan F. Beardon and
David Minda On the Pointwise Limit of Complex
Analytic Functions . . . . . . . . . . . 289--297
S. C. Coutinho and
J. C. McConnell The Quest for Quotient Rings (Of
Noncommutative Noetherian Rings) . . . . 298--313
Yuval Peres and
Károly Simon and
Boris Solomyak Fractals with Positive Length and Zero
Buffon Needle Probability . . . . . . . 314--325
L. D. Servi Nested Square Roots of 2 . . . . . . . . 326--330
Nigel Boston Strategies for the Weakest Link . . . . 330--334
Mitsuru Uchiyama Proofs of Korovkin's Theorems via
Inequalities . . . . . . . . . . . . . . 334--336
Peter Walker The Zeros of the Partial Sums of the
Exponential Series . . . . . . . . . . . 337--339
Marty Getz and
Dixon Jones Problem 11005 . . . . . . . . . . . . . 340--340
Bogdan Suceav\ua Problem 11006 . . . . . . . . . . . . . 340--340
Western Maryland College Problems Group Problem 11007 . . . . . . . . . . . . . 340--340
José Luis Díaz-Barrero and
Juan José Egozcue Problem 11008 . . . . . . . . . . . . . 340--340
David Borwein and
Jonathan M. Borwein and
Jamal Rooin Problem 11009 . . . . . . . . . . . . . 341--341
Erwin Just and
Norman Schaumberger Problem 11010 . . . . . . . . . . . . . 341--341
George Lamb Problem 11011 . . . . . . . . . . . . . 341--341
Zoltán Sasvári and
Richard Stong Approximating the Binomial Distribution:
10876 . . . . . . . . . . . . . . . . . 341--342
Pál Péter Dályay and
Said Amghibech and
David Callan Another Binomial Coefficient Identity:
10878 . . . . . . . . . . . . . . . . . 342--343
Nick MacKinnon and
John C. Cock Tiling Squares with Rectangles: 10883 343--344
Joaquín Gómez Rey and
Albert Nijenhuis and
Doyle Henderson and
Damuele Riccarelli and
Richard Stong An Unexpected Integer: 10886 . . . . . . 344--345
Jean Anglesio and
Said Amghibech and
GCHQ Problem Solving Group Six Incenters on a Conic: 10887 . . . . 346--347
William P. Wardlaw and
William D. Withers and
Ellen Hertz and
Horst Brunotte and
GCHQ Problem Solving Group Homomorphisms of Quasigroups: 10888 . . 347--347
Richard Montgomery Book Review: \booktitle[untitled] . . . 348--353
Jeffrey Rauch Book Review: \booktitle[untitled] . . . 353--357
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 358--359
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Charles Livingston Enhanced Linking Numbers . . . . . . . . 361--385
Mourad Ba\"\iou and
Michel Balinski Admissions and Recruitment . . . . . . . 386--399
János Pach and
Rom Pinchasi How Many Unit Equilateral Triangles Can
Be Generated by N Points in Convex
Position? . . . . . . . . . . . . . . . 400--406
Byron Schmuland Random Harmonic Series . . . . . . . . . 407--416
Hud Hudson Four Colors Do Not Suffice . . . . . . . 417--423
John Duncan and
Colin M. McGregor Carleman's Inequality . . . . . . . . . 424--431
M. A. Nyblom A Note on the Solvability of a
Diophantine Equation Involving Radicals 431--434
Jonathan Sondow Zeros of the Alternating Zeta Function
on the Line R(S) = 1 . . . . . . . . . . 435--437
C\ualin Popescu Problem 11012 . . . . . . . . . . . . . 438--438
David Callan Problem 11013 . . . . . . . . . . . . . 438--438
Achilleas Sinefakopoulos Problem 11014 . . . . . . . . . . . . . 438--438
Ovidiu Furdui Problem 11015 . . . . . . . . . . . . . 438--438
Juan-Boscoa Romero Márquez Problem 11016 . . . . . . . . . . . . . 439--439
C. R. Pranesachar Problem 11017 . . . . . . . . . . . . . 439--439
Slavko Simic Problem 11018 . . . . . . . . . . . . . 439--439
Roland Bacher and
Albert Nijenhuis A Surprisingly Simple Determinant: 10891 439--440
Stephen C. Locke and
Richard Stong Spanning Cycles in Hypercubes: 10892 . . 440--441
Andrei Jorza and
John H. Lindsey II and
Anne-Maria Ernvall and
Reijo Ernvall Groups of Divisors: 10893 . . . . . . . 441--443
Robert Sulanke and
Jose Luis Arregui and
Danijela Vuji\'c and
Nelson Castañeda and
David Callan Another Description of the Central
Delannoy Numbers: 10894 . . . . . . . . 443--444
Christopher J. Hillar and
Patrick J. Fitzsimmons Convergent Series with Exponents: 10928 444--445
Jet Wimp and
Kenneth Schilling Serendipitous Solution: 10428 . . . . . 445--445
A. W. Knapp Book Review: \booktitle[untitled] . . . 446--455
Marion Cohen Book Review: \booktitle[untitled] . . . 455--458
Anonymous Telegraphic Reviews . . . . . . . . . . 459--461
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Steven G. Krantz A Matter of Gravity . . . . . . . . . . 465--481
Godfried Toussaint Simple Proofs of a Geometric Property of
Four-Bar Linkages . . . . . . . . . . . 482--494
Robin Hartshorne Non-Euclidean III.36 . . . . . . . . . . 495--502
Franklin Mendivil Fractals, Graphs, and Fields . . . . . . 503--515
Tom M. Apostol and
Mamikon A. Mnatsakanian Sums of Squares of Distances in
$m$-Space . . . . . . . . . . . . . . . 516--526
Martin Klazar Counting Even and Odd Partitions . . . . 527--532
Dragan Vukoti\'c The Isoperimetric Inequality and a
Theorem of Hardy and Littlewood . . . . 532--536
Anton R. Schep And Still One More Proof of the
Radon--Nikodym Theorem . . . . . . . . . 536--538
Michael Somos and
Robert Haas A Linked Pair of Sequences Implies the
Primes Are Infinite . . . . . . . . . . 539--540
James D. Harper Another Simple Proof of $ 1 + 1 / 2^2 +
1 / 3^2 + \cdots = \pi^2 / 6 $ . . . . . 540--541
Bernardo Recamán Santos Problem 11019 . . . . . . . . . . . . . 542--542
M. L. Glasser Problem 11020 . . . . . . . . . . . . . 542--542
Donald E. Knuth Problem 11021 . . . . . . . . . . . . . 542--542
Razvan Satnoianu Problem 11022 . . . . . . . . . . . . . 542--542
Wu Wei Chao Problem 11023 . . . . . . . . . . . . . 542--542
Vicen\ctiu R\uadulescu Problem 11024 . . . . . . . . . . . . . 543--543
Floor van Lamoen and
Darij Grinberg Problem 11025 . . . . . . . . . . . . . 543--543
Rick Mabry Problem 11001 . . . . . . . . . . . . . 543--543
Wu Wei Chao and
Gerry Myerson Divisibility Conditions Holding as Many
Times as You Want: 10898 . . . . . . . . 543--544
Richard Bagby and
O. P. Lossers Best Polynomial Approximations: 10903 544--544
Zhibing Chen and
Shusen Ding A Higher Mean Value Theorem: 10935 . . . 544--545
Andor Lucács and
Szilard András and
Nathan D. Cahill Convex $n$-Gons: 10936 . . . . . . . . . 545--546
Yves Nievergelt and
Achava Nakhash The Complex Geometric Mean: 10940 . . . 546--547
Jeffrey C. Lagarias and
Thomas Hermann and
O. P. Lossers Decay of a Markov Chain: 10941 . . . . . 547--548
Ovidiu Furdui and
O. P. Lossers An Inequality for Triangles: 10950 . . . 548--549
David G. Schaeffer Book Review: \booktitle[untitled] . . . 550--553
Jeffrey L. Nunemacher Book Review: \booktitle[untitled] . . . 554--557
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Noam D. Elkies On the Sums $ \sum_{k = - \infty
}^\infty (4 k + 1)^{-n} $ . . . . . . . 561--573
Daniel K. Biss Which Functor Is the Projective Line? 574--592
Jerry Lodder Curvature in the Calculus Curriculum . . 593--605
Guershon Harel and
Jeffrey M. Rabin Polygons Whose Vertex Triangles Have
Equal Area . . . . . . . . . . . . . . . 606--619
Harm Derksen The Fundamental Theorem of Algebra and
Linear Algebra . . . . . . . . . . . . . 620--623
Charles Thas Projective Generalizations of Two Points
of Concurrence on the Nine-Point Circle 624--627
Ulrich Abel On the Lagrange Remainder of the Taylor
Formula . . . . . . . . . . . . . . . . 627--633
Jussi Väisälä A Proof of the Mazur--Ulam Theorem . . . 633--635
Jonathan Sondow Problem 11026 . . . . . . . . . . . . . 636--636
H. Reuvers Problem 11027 . . . . . . . . . . . . . 636--636
Götz Trenkler Problem 11028 . . . . . . . . . . . . . 636--636
Tim Keller Problem 11029 . . . . . . . . . . . . . 636--636
Steven Butler Problem 11030 . . . . . . . . . . . . . 637--637
Li Zhou Problem 11031 . . . . . . . . . . . . . 637--637
Mark Pinsky Problem 11032 . . . . . . . . . . . . . 637--637
Torben Maack Bisgaard and
Zsolt Páles and
Zoltán Sasvári and
Richard Bagby Determinant of a Matrix in Two
Variables: 10896 . . . . . . . . . . . . 637--638
Gregory P. Wene and
Robin Chapman Generators of Ideals of Matrices over
Finite Fields: 10897 . . . . . . . . . . 638--639
Gordon Rice and
Patrick A. Staley and
Gerald Myerson and
Robin Chapman Angles with Rational Cosines: 10900 . . 639--639
Emeric Deutsch and
Nasha Komanda Derangements That Don't Rise Too Fast:
10902 . . . . . . . . . . . . . . . . . 639--640
Richard P. Stanley and
Robin Chapman An Unexpected Appearance of the Catalan
Numbers: 10905 . . . . . . . . . . . . . 640--642
Donald E. Knuth and
C. P. Rupert and
Alex Smith and
Richard Stong Recounting the Rationals, Continued:
10906 . . . . . . . . . . . . . . . . . 642--643
John H. Hubbard Book Review: \booktitle[untitled] . . . 644--649
Marion D. Cohen Book Review: \booktitle[untitled] . . . 650--652
Ranjan Roy Book Review: \booktitle[untitled] . . . 652--657
Anonymous Telegraphic Reviews . . . . . . . . . . 658--660
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Charles W. Curtis Richard Brauer: Sketches from His Life
and Work . . . . . . . . . . . . . . . . 665--678
Hans Havlicek and
Gunter Weiß Altitudes of a Tetrahedron and Traceless
Quadratic Forms . . . . . . . . . . . . 679--693
Daniel J. Acosta Newton's Rule of Signs for Imaginary
Roots . . . . . . . . . . . . . . . . . 694--706
Matthias Beck and
Moshe Cohen and
Jessica Cuomo and
Paul Gribelyuk The Number of ``Magic'' Squares, Cubes,
and Hypercubes . . . . . . . . . . . . . 707--717
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-Third William Lowell Putnam
Mathematical Competition . . . . . . . . 718--726
Razvan A. Satnoianu Erd\Hos--Mordell-Type Inequalities in a
Triangle . . . . . . . . . . . . . . . . 727--729
Chris Impens Stirling's Series Made Easy . . . . . . 730--735
Nicolas Lichiardopol A New Proof of Wedderburn's Theorem . . 736--737
Karim Boulabiar and
Gerard Buskes After the Determinants Are down: a
Criterion for Invertibility . . . . . . 737--741
M. N. Deshpande and
R. M. Welukar Problem 11033 . . . . . . . . . . . . . 742--742
William P. Wardlaw Problem 11034 . . . . . . . . . . . . . 742--742
Omer Yayenie Problem 11035 . . . . . . . . . . . . . 742--742
M. L. Glasser Problem 11036 . . . . . . . . . . . . . 743--743
M. L. J. Hautus Problem 11037 . . . . . . . . . . . . . 743--743
Floor van Lamoen Problem 11038 . . . . . . . . . . . . . 743--743
Noah Rosenberg and
Richard Stong Problem 11039 . . . . . . . . . . . . . 743--743
Greg Martin and
Jonathan Bloom and
Dan Saracino Three Proper Subgroups Covering a Group:
10911 . . . . . . . . . . . . . . . . . 743--744
Jean Anglesio and
Kenneth F. Andersen A Recursively Defined Series for $ \pi /
4 $: 10912 . . . . . . . . . . . . . . . 744--745
Giovanni Falcone and
Richard Stong and
Nasha Komanda A Combination of Cyclotomic Polynomials:
10914 . . . . . . . . . . . . . . . . . 745--746
Gertrude Ehrlich and
Reiner Martin The Jug Problem with a Source and a
Sink: 10916 . . . . . . . . . . . . . . 746--746
Mathias Beck and
Nasha Komanda A Congruence Involving Ceilings: 10918 746--747
André Kündgen and
Radhika Ramamurthi and
Reiner Martin Maximal Paths in Bipartite Graphs: 10920 747--747
Marcin Mazur and
Roberto Tauraso and
Michel Bataille A Root Inequality: 10944 . . . . . . . . 747--749
Alex Kasman Book Review: \booktitle[untitled] . . . 750--754
Warwick Tucker Book Review: \booktitle[untitled] . . . 754--759
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Iva\"\ilo M. Mladenov and
John Oprea The Mylar Balloon Revisited . . . . . . 761--784
Karanbir S. Sarkaria Tetrahedron ABCD of Width 1 with Minimum
AB + BC + CD . . . . . . . . . . . . . . 785--799
Stephen McAdam Bell's Theorem and the Demise of Local
Reality . . . . . . . . . . . . . . . . 800--811
Chris Groër The Mathematics of Survival: From
Antiquity to the Playground . . . . . . 812--825
Kamal Poorrezaei Two Proofs of Graves's Theorem . . . . . 826--830
Jeongseon Baek and
Dong-Soo Kim and
Young Ho Kim A Characterization of the Unit Sphere 830--833
Michael W. Botsko An Elementary Proof of Lebesgue's
Differentiation Theorem . . . . . . . . 834--838
Nikita Sidorov Almost Every Number Has a Continuum of $
\beta $-Expansions . . . . . . . . . . . 838--842
Yongge Tian Problem 11040 . . . . . . . . . . . . . 843--843
Oscar Ciaurri Problem 11041 . . . . . . . . . . . . . 843--843
M. N. Deshpande and
Kavita Laghate Problem 11042 . . . . . . . . . . . . . 843--844
Michael Golomb Problem 11043 . . . . . . . . . . . . . 844--844
Michel Bataille Problem 11044 . . . . . . . . . . . . . 844--844
Manoj Prakash Singh Problem 11045 . . . . . . . . . . . . . 844--844
Christoph Soland Problem 11046 . . . . . . . . . . . . . 844--844
Donald E. Knuth and
Reiner Martin Products of Transpositions: 10913 . . . 844--845
C. P. Rupert and
Richard Stong A Sequence of Integer Polynomials: 10915 845--845
Lajos Csete and
Li Zhou Distances to the Sides: 10929 . . . . . 845--846
Vasile Mihai and
Li Zhou A Tetrahedron with All Faces Congruent:
10934 . . . . . . . . . . . . . . . . . 846--847
Aleksandar Ivi\'c Zetafunctionology: 10939 . . . . . . . . 847--848
Slavko Simic and
Said Amghibech An Appell-ing Inequality: 10945 . . . . 848--849
Stevo Stevi\'c and
Allen Stenger Asymptotics of a Recurrence: 10946 . . . 849--850
Rudy Rucker Book Review: \booktitle[untitled] . . . 851--861
Krishnaswami Alladi Book Review: \booktitle[untitled] . . . 861--865
Anonymous Telegraphic Reviews . . . . . . . . . . 866--868
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Daniel Drucker and
Stephen A. Williams When Does Water Find the Shortest Path
Downhill? The Geometry of Steepest
Descent Curves . . . . . . . . . . . . . 869--885
Susanna S. Epp The Role of Logic in Teaching Proof . . 886--899
Allan Pinkus Negative Theorems in Approximation
Theory . . . . . . . . . . . . . . . . . 900--911
Richard E. Chandler and
Carl D. Meyer and
Nicholas J. Rose Eudoxus Meets Cayley . . . . . . . . . . 912--927
Frank Blume A Localized Probabilistic Approach to
Circuit Analysis . . . . . . . . . . . . 928--936
Inta Bertuccioni A Topological Puzzle . . . . . . . . . . 937--939
David C. Ullrich The Ascoli--Arzel\`a Theorem via
Tychonoff's Theorem . . . . . . . . . . 939--940
PL. Kannappan Klee's Trigonometry Problem . . . . . . 940--944
Paul Loya Green's Theorem and the Fundamental
Theorem of Algebra . . . . . . . . . . . 944--946
Dominique Hulin and
Marc Troyanov Mean Curvature and Asymptotic Volume of
Small Balls . . . . . . . . . . . . . . 947--950
C. W. Groetsch Timing Is Everything: The French
Connection . . . . . . . . . . . . . . . 950--955
Syrous Marivani Problem 11047 . . . . . . . . . . . . . 956--956
Matthias Beck and
Marcin Mazur and
Shelemyahu Zacks Problem 11048 . . . . . . . . . . . . . 956--956
Vasile Mihai Problem 11049 . . . . . . . . . . . . . 956--956
Kent Holing Problem 11050 . . . . . . . . . . . . . 957--957
Nick MacKinnon Problem 11051 . . . . . . . . . . . . . 957--957
Danrun Huang and
Daniel Scully Problem 11052 . . . . . . . . . . . . . 957--957
Wu Wei Chao Problem 11053 . . . . . . . . . . . . . 958--958
David M. Bloom and
Christopher N. Swanson and
Kenneth Schilling A Convolution of Middle Binomial
Coefficients: 10921 . . . . . . . . . . 958--959
Mizan R. Khan and
Michael R. Avidon The Sum of Divisors Won't Die: 10922 . . 959--959
David Callan and
Harris Kwong A Permanent Fixture: 10925 . . . . . . . 960--960
Harold G. Diamond and
Li Zhou A Continued Fraction for an Arctan
Difference: 10926 . . . . . . . . . . . 960--961
Jean-Pierre Grivaux and
Allen Stenger and
J. Ernest Wilkins Jr. A Rational Definite Integral: 10938 . . 961--962
Erwin Just and
Norman Schaumberger and
Albert Stadler Points on a Circle: 10954 . . . . . . . 962--963
Anonymous Erratum: Anagrammatical Attribution:
11021 . . . . . . . . . . . . . . . . . 963--963
Ed Waymire Book Review: \booktitle[untitled] . . . 964--967
Marion D. Cohen Book Review: \booktitle[untitled] . . . 968--969
Daniel Gottesman Book Review: \booktitle[untitled] . . . 969--972
Anonymous Volume Information . . . . . . . . . . . 973--984
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Ivor Grattan-Guinness History or Heritage? An Important
Distinction in Mathematics and for
Mathematics Education . . . . . . . . . 1--12
Michael A. Bennett and
Bruce Reznick Positive Rational Solutions to $ x^y =
y^{m x} $: a Number-Theoretic Excursion 13--21
Richard P. Jerrard and
John E. Wetzel Prince Rupert's Rectangles . . . . . . . 22--31
Steven G. Krantz and
Jeffery D. McNeal Creating More Convergent Series . . . . 32--38
Burkard Polster Variations on a Theme in Paper Folding 39--47
Sey Y. Kim An Elementary Proof of the Quadratic
Reciprocity Law . . . . . . . . . . . . 48--50
Götz Trenkler Matrices Which Take a Given Vector into
a Given Vector: Revisited . . . . . . . 50--52
Thomas J. Osler Finding $ \zeta (2 p) $ from a Product
of Sines . . . . . . . . . . . . . . . . 52--54
S. H. Kulkarni A Very Simple and Elementary Proof of a
Theorem of Ingelstam . . . . . . . . . . 54--58
W. A. Beyer and
Andrew Zardecki The Early History of the Ham Sandwich
Theorem . . . . . . . . . . . . . . . . 58--61
Alexander R. Perlis Roots Appear in Quanta . . . . . . . . . 61--63
Shahin Amrahov Problem 11054 . . . . . . . . . . . . . 64--64
Razvan Satnoianu Problem 11055 . . . . . . . . . . . . . 64--64
John H. Lindsey II Problem 11056 . . . . . . . . . . . . . 64--64
Zahlreich Problems Group Problem 11057 . . . . . . . . . . . . . 64--64
Óscar Ciaurri Problem 11058 . . . . . . . . . . . . . 64--64
Mark Bowron Problem 11059 . . . . . . . . . . . . . 64--65
Matthew Coppenbarger Problem 11060 . . . . . . . . . . . . . 65--65
Peter Walker and
Tom Zerger The Centroid-Circumcenter Distance:
10948 . . . . . . . . . . . . . . . . . 65--66
Leroy Quet and
GCHQ Problem Solving Group Functionally Related Convergents: 10953 66--67
Razvan Satnoianu and
Isaac Sofair More Triangle Inequalities: 10955 . . . 67--69
George L. Lamb and
Stephen J. Herschkorn Hypergeometric and Other
Representations: 10959 . . . . . . . . . 69--71
Mihály Bencze and
Li Zhou Cosine Inequalities: 10962 . . . . . . . 71--71
Anthony Ralston Book Review: \booktitle[untitled] . . . 72--75
Anonymous [untitled] . . . . . . . . . . . . . . . 75--81
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 82--84
Anonymous Back Matter . . . . . . . . . . . . . . 85--88
Anonymous Front Matter . . . . . . . . . . . . . . ??
Susan Landau Polynomials in the Nation's Service:
Using Algebra to Design the Advanced
Encryption Standard . . . . . . . . . . 89--117
Tom M. Apostol and
Mamikon A. Mnatsakanian Isoperimetric and Isoparametric Problems 118--136
Charles Radin Orbits of Orbs: Sphere Packing Meets
Penrose Tilings . . . . . . . . . . . . 137--149
Fabrizio Zanello When Are There Infinitely Many
Irreducible Elements in a Principal
Ideal Domain? . . . . . . . . . . . . . 150--152
David Avis and
Bohdan Kaluzny Solving Inequalities and Proving
Farkas's Lemma Made Easy . . . . . . . . 152--157
Suk-Geun Hwang Cauchy's Interlace Theorem for
Eigenvalues of Hermitian Matrices . . . 157--159
Michael Schmitt New Designs for the Descartes Rule of
Signs . . . . . . . . . . . . . . . . . 159--164
Wu Wei Chao Problem 11061 . . . . . . . . . . . . . 165--165
Kenneth Schilling Problem 11062 . . . . . . . . . . . . . 165--165
Slavko Simic Problem 11063 . . . . . . . . . . . . . 165--165
John Wetzel Problem 11064 . . . . . . . . . . . . . 165--165
Anonymous Correction: 11034 . . . . . . . . . . . 166--166
Douglas B. Tyler Problem 11065 . . . . . . . . . . . . . 166--166
Sebastian Cioab\ua Problem 11066 . . . . . . . . . . . . . 166--166
George Lamb Problem 11067 . . . . . . . . . . . . . 166--166
Donald E. Knuth and
Robin Chapman Fibonacci in Complex Camouflage: 10858 166--167
Jeffrey C. Lagarias and
E. M. Rains and
N. J. A. Sloane and
Nasha Komanda The EKG Sequence: 10927 . . . . . . . . 167--168
Paul Schweitzer and
Xiaoshen Wang and
National Security Agency Problems Group Too Much Commuting: 10930 . . . . . . . 168--169
Robert DeSario and
LeRoy Wenstrom Invertible Shuffles: 10931 . . . . . . . 169--170
Paul Lescott and
Tom Jager A Group Determined by Relations?: 10933 170--171
David G. Wagner and
Patrick Corn and
Li Zhou A Cyclotomic Sum: 10937 . . . . . . . . 171--172
Victor Alexandrov and
Knut Dale Using Stokes's Theorem on the Sphere:
10957 . . . . . . . . . . . . . . . . . 172--172
Steven R. Bell Book Review: \booktitle[untitled] . . . 173--176
Margaret M. Bayer Book Review: \booktitle[untitled] . . . 177--180
Anonymous Back Matter . . . . . . . . . . . . . . 181--184
Anonymous Front Matter . . . . . . . . . . . . . . ??
Robert E. Megginson Yueh-Gin Gung and Dr. Charles Y. Hu
Award to T. Christine Stevens for
Distinguished Service to Mathematics . . 185--188
Alan Edelman and
Gilbert Strang Pascal Matrices . . . . . . . . . . . . 189--197
William T. Ingram and
William S. Mahavier Interesting Dynamics and Inverse Limits
in a Family of One-Dimensional Maps . . 198--215
Jaume Paradís and
Josep Pla and
Pelegrí Viader Fermat and the Quadrature of the Folium
of Descartes . . . . . . . . . . . . . . 216--229
Detlef Gronau The Spiral of Theodorus . . . . . . . . 230--237
Leslie Blackwell Galen Putting Fractions in Their Place . . . . 238--242
Tsuneo Ishikawa and
Nobuhiko Ishida and
Yoshito Yukimoto On Prime Factors of $ A^n - 1 $ . . . . 243--245
Lou M. Pretorius and
Konrad J. Swanepoel An Algorithmic Proof of the
Motzkin--Rabin Theorem on Monochrome
Lines . . . . . . . . . . . . . . . . . 245--251
Martin Engman A Note on Isometric Embeddings of
Surfaces of Revolution . . . . . . . . . 251--255
T. Y. Lam On Subgroups of Prime Index . . . . . . 256--258
Herbert Wilf Problem 11068 . . . . . . . . . . . . . 259--259
Péter Ivády Problem 11069 . . . . . . . . . . . . . 259--259
Roberto Tauraso Problem 11070 . . . . . . . . . . . . . 259--259
Emeric Deutsch Problem 11071 . . . . . . . . . . . . . 259--259
George Lamb Problem 11072 . . . . . . . . . . . . . 259--259
Vicen\ctiu R\uadulescu Problem 11073 . . . . . . . . . . . . . 260--260
Dimiter Skordev Problem 11074 . . . . . . . . . . . . . 260--260
Roland Bacher and
Robin Chapman and
Reiner Martin A Determinant of Indeterminates: 10859 260--261
Jürgen Groß and
Götz Trenkler and
Xiaoshen Wang Product and Sum of Projections: 10917 261--262
Christian Bey and
Garth Isaak Maximum Antichains of Sets of Distinct
Sizes: 10932 . . . . . . . . . . . . . . 262--263
Walther Janous and
J. P. V. Abad Maximum Antichains in the Divisor
Lattice: 10942 . . . . . . . . . . . . . 263--263
C\ualin Popescu and
GCHQ Problem Solving Group A Divisibility Result: 10943 . . . . . . 264--264
Jeffrey Lagarias and
Walther Janous A Generous Bound for Divisor Sums: 10949 264--265
David Callan and
M. A. Prasad Counting a Set of Rooted Trees: 10952 265--266
Brian Conrad and
Gheorge Simion and
Patrick Corn Pi and Rationals: 10961 . . . . . . . . 266--266
John B. Little Book Review: \booktitle[untitled] . . . 267--271
Stephen A. Fulling Book Review: \booktitle[untitled] . . . 271--275
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 276--278
Anonymous Back Matter . . . . . . . . . . . . . . 279--280
Anonymous Front Matter . . . . . . . . . . . . . . ??
Roe Goodman Alice through Looking Glass after
Looking Glass: The Mathematics of
Mirrors and Kaleidoscopes . . . . . . . 281--298
Geoffrey Grimmett Stochastic Apportionment . . . . . . . . 299--307
Pirooz Mohazzabi and
Thomas A. Fournelle Evaluation of Ill-Behaved Power Series 308--321
Curtis D. Bennett and
A. M. W. Glass and
Gábor J. Székely Fermat's Last Theorem for Rational
Exponents . . . . . . . . . . . . . . . 322--329
Bruce C. Berndt and
C. A. Reddi Two Exams Taken by Ramanujan in India 330--339
Asuman Aksoy and
Mario Martelli The Wave Equation, Mixed Partial
Derivatives, and Fubini's Theorem . . . 340--347
Dov Samet and
Iddo Samet and
David Schmeidler One Observation behind Two-Envelope
Puzzles . . . . . . . . . . . . . . . . 347--351
E. Kowalski On the ``Reducibility'' of Arctangents
of Integers . . . . . . . . . . . . . . 351--354
Paul Monsky Kepler's First Law: a Remark . . . . . . 355--356
Hervé Perdry An Elementary Proof of Krull's
Intersection Theorem . . . . . . . . . . 356--357
Jacob Mostovoy Lattices in $ \mathbb {C} $ and Finite
Subsets of a Circle . . . . . . . . . . 357--360
Götz Trenkler Problem 11075 . . . . . . . . . . . . . 361--361
Joel Zinn Problem 11076 . . . . . . . . . . . . . 361--361
Gheorge Costovici Problem 11077 . . . . . . . . . . . . . 361--361
Donald Knuth Problem 11078 . . . . . . . . . . . . . 361--361
Brian Cook and
James Whitenton Problem 11079 . . . . . . . . . . . . . 361--362
Razvan Satnoianu Problem 11080 . . . . . . . . . . . . . 362--362
Stephen Morse Problem 11081 . . . . . . . . . . . . . 362--362
LSU Problem Solving Group and
Marc A. Chamberland A Sequence of Composite Numbers: 10947 362--363
Sung Soo Kim and
Li Zhou A Sticky Problem: 10951 . . . . . . . . 363--364
John McCarthy and
Lee Badger and
Marc Williams The Tower of Stanford: 10956 . . . . . . 364--365
Oliver Eng and
Li Zhou Sliding Dominoes: 10960 . . . . . . . . 365--366
M. L. Glosser and
J. A. Grzesik A Nontrivial Zero.: 11020 . . . . . . . 366--367
Vicen\ctiu R\uadulescu and
Richard Stong A Limit Problem: 11024 . . . . . . . . . 367--368
Daniel R. Farkas Book Review: \booktitle[untitled] . . . 369--372
Paul Zorn Book Review: \booktitle[untitled] . . . 373--375
Anonymous Back Matter . . . . . . . . . . . . . . 376--376
Anonymous Front Matter . . . . . . . . . . . . . . ??
Donald G. Saari Geometry of Chaotic and Stable
Discussions . . . . . . . . . . . . . . 377--393
Maya Mohsin Ahmed How Many Squares Are There, Mr.
Franklin?: Constructing and Enumerating
Franklin Squares . . . . . . . . . . . . 394--410
Barbara S. Edwards and
Michael B. Ward Surprises from Mathematics Education
Research: Student (Mis)use of
Mathematical Definitions . . . . . . . . 411--424
Jeroen Spandaw Dissecting Cuboids into Cuboids . . . . 425--429
Hirofumi Tsumura An Elementary Proof of Euler's Formula
for $ \zeta (2 m) $ . . . . . . . . . . 430--431
Grzegorz Rz\kadkowski A Short Proof of the Explicit Formula
for Bernoulli Numbers . . . . . . . . . 432--434
Raymond T. Boute Moving a Rectangle around a Corner:
Geometrically . . . . . . . . . . . . . 435--437
Christoph Leuenberger An Old Friend Revisited . . . . . . . . 437--439
Wu Wei Chao Problem 11082 . . . . . . . . . . . . . 440--440
William P. Wardlaw Problem 11083 . . . . . . . . . . . . . 440--440
H. A. ShahAli Problem 11084 . . . . . . . . . . . . . 440--440
Matthias Beck and
Jesus DeLoera and
Mike Develin and
Julian Pfeifle Problem 11085 . . . . . . . . . . . . . 440--440
Stephen C. Locke Problem 11086 . . . . . . . . . . . . . 440--441
Robin Chapman and
Nicholas C. Singer Eigenvalues of a Bidiagonal Matrix:
10958 . . . . . . . . . . . . . . . . . 441--441
Michael Golomb Problem 11087 . . . . . . . . . . . . . 441--441
Richard Holzsager Problem 11088 . . . . . . . . . . . . . 441--441
Paul Deiermann and
Cape Girardeau and
Joseph Chalmers and
George L. Lamb, Jr. An Application of the Mellin Transform:
10963 . . . . . . . . . . . . . . . . . 441--443
Douglas B. West and
Csaba Megyeri Adjacency Matrices That Are Incidence
Matrices: 10967 . . . . . . . . . . . . 443--443
Stephen C. Locke and
Philip D. Straffin The Game of Pathos: 10968 . . . . . . . 443--444
Vitaly Voloshin and
José Heber Nieto and
Edward R. Scheinerman and
Robin Chapman Plucking Stirling Numbers from Trees:
10976 . . . . . . . . . . . . . . . . . 444--445
Carl Axness and
Bert Kerr and
Jean-François Chamayou Incomplete Gamma and Error Functions:
10977 . . . . . . . . . . . . . . . . . 445--447
Donald Knuth and
BSI Problems Group Some Bernstein Polynomials: 10985 . . . 447--447
G. E. Fasshauer Book Review: \booktitle[untitled] . . . 448--452
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 453--455
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 456--460
Anonymous Back Matter . . . . . . . . . . . . . . 461--464
Anonymous Front Matter . . . . . . . . . . . . . . ??
David E. Zitarelli The Origin and Early Impact of the Moore
Method . . . . . . . . . . . . . . . . . 465--486
Henry Cohn Projective Geometry over $ \mathbb {F}_1
$ and the Gaussian Binomial Coefficients 487--495
Tom M. Apostol and
Mamikon A. Mnatsakanian A Fresh Look at the Method of Archimedes 496--508
Casey Mann Heesch's Tiling Problem . . . . . . . . 509--517
Gilbert Helmberg A Construction Concerning $ (l^p)^\prime
\subset l^q $ . . . . . . . . . . . . . 518--520
Kehe Zhu Translating Inequalities between Hardy
and Bergman Spaces . . . . . . . . . . . 520--525
Xiaoshen Wang A Simple Proof of Descartes's Rule of
Signs . . . . . . . . . . . . . . . . . 525--526
Sam B. Nadler, Jr. Another Proof That $ R^3 $ Has No Square
Root . . . . . . . . . . . . . . . . . . 527--528
Steven H. Weintraub An Interesting Recursion . . . . . . . . 528--530
Gregory P. Dresden On the Middle Coefficient of a
Cyclotomic Polynomial . . . . . . . . . 531--533
Sun Soo Kim Problem 11089 . . . . . . . . . . . . . 534--534
Florian Luca Problem 11090 . . . . . . . . . . . . . 534--534
David Callan Problem 11091 . . . . . . . . . . . . . 534--534
Arturo Magidin Problem 11092 . . . . . . . . . . . . . 534--535
Richard Bagby Problem 11093 . . . . . . . . . . . . . 535--535
Michel Bataille Problem 11094 . . . . . . . . . . . . . 535--535
Vasile Mihai Problem 11095 . . . . . . . . . . . . . 535--535
H. A. ShahAli and
Hamza Ahmad Graceful Permutations Revisited: 10964 535--536
Jean-Marie De Koninck and
Stefan Gubo When the Totient Is the Product of the
Squared Prime Divisors: 10966 . . . . . 536--536
Richard Stanley and
O. P. Lossers Comparing Odd Parts in Conjugate
Partitions: 10969 . . . . . . . . . . . 536--539
C. P. Rupert and
Richard Stong The First Fibonacci Number Divisible by
a Prime p: 10971 . . . . . . . . . . . . 539--540
Tim Ferguson and
M. D. Frederick and
Lenny Jones and
Stephen M. Gagola, Jr. The LCM of the Parts of a Partition:
10972 . . . . . . . . . . . . . . . . . 540--541
Emeric Deutsch and
Julio Kuplinsky and
Tina Garrett Enumeration of Permutations by Disorder:
10975 . . . . . . . . . . . . . . . . . 541--541
Douglas R. Shier Book Review: \booktitle[untitled] . . . 542--545
Anonymous Back Matter . . . . . . . . . . . . . . 546--548
Anonymous Front Matter . . . . . . . . . . . . . . ??
Joan R. Leitzel The 2003 James R. C. Leitzel Lecture:
Mathematics' Response to Issues in
Higher Education . . . . . . . . . . . . 549--558
Reinhard Diestel On Infinite Cycles in Graphs: Or How to
Make Graph Homology Interesting . . . . 559--571
Torsten Ekedahl and
Dan Laksov Two ``Generic'' Proofs of the Spectral
Mapping Theorem . . . . . . . . . . . . 572--585
Federico Ardila The Number of Halving Circles . . . . . 586--591
Darko Veljan Geometry and Convexity of $ \cos {\sqrt
{x}} $ . . . . . . . . . . . . . . . . . 592--595
Bau-Sen Du A Simple Proof of Sharkovsky's Theorem 595--599
Tyler Jarvis and
James Tanton The Hairy Ball Theorem via Sperner's
Lemma . . . . . . . . . . . . . . . . . 599--603
Kenzi Satô Some Subgroups of $ {\rm SO}_3 (\mathbb
{R}) $ Isomorphic to the Free Product $
(\mathbb {Z} / 2 \mathbb {Z}) \ast
(\mathbb {Z} / 3 \mathbb {Z}) $ . . . . 603--607
V. I. Arnol'd From Hilbert's Superposition Problem to
Dynamical Systems . . . . . . . . . . . 608--624
Said Amghibech Problem 11096 . . . . . . . . . . . . . 625--625
Kevin Ford Problem 11097 . . . . . . . . . . . . . 625--625
Christopher Hillar and
Darren Rhea Problem 11098 . . . . . . . . . . . . . 625--625
Matthias Beck and
Richard Ehrenborg and
Thomas Zaslavsky Problem 11099 . . . . . . . . . . . . . 625--626
C\ualin Popescu Problem 11100 . . . . . . . . . . . . . 626--626
Earl F. Skelton Problem 11101 . . . . . . . . . . . . . 626--626
Leroy Quet Problem 11102 . . . . . . . . . . . . . 626--626
Razvan Satnoianu and
John G. Heuver Comparison of Some Squared Distances:
10970 . . . . . . . . . . . . . . . . . 626--627
L. D. Servi and
Richard Stong A Disguised Half-Angle Iteration: 10973 627--628
Syrous Marivani and
Bill Mixon Digital Roots of Fibonacci Numbers:
10974 . . . . . . . . . . . . . . . . . 628--628
Emeric Deutsch and
Julio Kuplinsky and
Tina Garrett Enumeration of Permutations by Disorder:
10975 . . . . . . . . . . . . . . . . . 628--629
Jean-Pierre Grivaux and
Tsehaye Andebrhan Nonnegative Polynomials: 10978 . . . . . 629--630
Donald P. Minassian and
K. P. Hart Simple Discontinuities: 10979 . . . . . 630--630
Nicholas C. Singer A Divisibility Property of a Recurrence:
10981 . . . . . . . . . . . . . . . . . 631--631
Yuming Chen and
Olaf Krafft and
Martin Schaefer Variation of a Ukrainian Olympiad
Problem: 10982 . . . . . . . . . . . . . 631--632
Herbert Wilf and
J. A. Grzesik An Arc Cotangent Series: 10986 . . . . . 632--632
David W. Boyd Book Review: \booktitle[untitled] . . . 633--636
Arthur T. Benjamin Book Review: \booktitle[untitled] . . . 636--638
Arnold Ostebee Telegraphic Reviews . . . . . . . . . . 639--641
Anonymous Back Matter . . . . . . . . . . . . . . 642--644
Anonymous Front Matter . . . . . . . . . . . . . . ??
Steven R. Finch and
John E. Wetzel Lost in a Forest . . . . . . . . . . . . 645--654
Olga Holtz and
Volker Mehrmann and
Hans Schneider Potter, Wielandt, and Drazin on the
Matrix Equation $ A B = \omega B A $:
New Answers to Old Questions . . . . . . 655--667
Joel Anderson Iterated Exponentials . . . . . . . . . 668--679
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-Fourth William Lowell Putnam
Mathematical Competition . . . . . . . . 680--690
Joseph A. Gallian The First Sixty-Six Years of the Putnam
Competition . . . . . . . . . . . . . . 691--699
Kenneth Glass and
Chi-Keung Ng A Simple Proof of the Hook Length
Formula . . . . . . . . . . . . . . . . 700--704
R. L. Devaney and
K. Josi\'c and
M. Moreno Rocha and
P. Seal and
Y. Shapiro and
A. T. Frumosu Playing Catch-up with Iterated
Exponentials . . . . . . . . . . . . . . 704--709
Daniel A. Klain An Intuitive Derivation of Heron's
Formula . . . . . . . . . . . . . . . . 709--712
Lars Olsen A New Proof of Darboux's Theorem . . . . 713--715
M. F. Atiyah Bakerian Lecture, 1975: Global Geometry 716--723
Gregory Galperin and
Hillel Gauchman Problem 11103 . . . . . . . . . . . . . 724--724
Vicen\ctiu R\uadulescu Problem 11104 . . . . . . . . . . . . . 724--724
Juan-Bosco Romero Marquez and
Rick Luttmann and
Miguel de Guzman and
G. Donald Chakerian Problem 11105 . . . . . . . . . . . . . 724--725
David Callan Problem 11106 . . . . . . . . . . . . . 725--725
Michel Émery Problem 11107 . . . . . . . . . . . . . 725--725
Emeric Deutsch Problem 11108 . . . . . . . . . . . . . 725--725
Solomon W. Golomb Problem 11109 . . . . . . . . . . . . . 725--725
Matthias Beck and
Jesus DeLoera and
Mike Develin and
Julian Pfeifle Problem 11085 . . . . . . . . . . . . . 725--725
Wu Wei Chao and
Doyle Henderson Continuous Additive Functions: 10854 . . 725--726
John Melville and
Jason Heller and
Stony Brook A Classic Pointed Triangle Inequality:
10965 . . . . . . . . . . . . . . . . . 726--726
Bogdan Suceav\ua and
C. G. Petalas and
T. P. Vidalis Orthocenter Projection: 10983 . . . . . 726--728
Yongge Tian and
Carl Meyer Injective Properties of Complex
Matrices: 10984 . . . . . . . . . . . . 728--728
Kumar N. Prasanna and
B. G. Shenoy and
J. A. Grzesik Polynomial Nullstellen Avoidance: 10987 729--729
Wu Wei Chao and
Doyle Henderson and
John H. Lindsey, II An Iterative Sequence: 10988 . . . . . . 729--731
Steven G. Krantz Book Review: \booktitle[untitled] . . . 732--735
Marion D. Cohen Book Review: \booktitle[untitled] . . . 735--738
Anonymous Back Matter . . . . . . . . . . . . . . 739--740
Anonymous Front Matter . . . . . . . . . . . . . . ??
Colin Adams and
Thomas Fleming and
Christopher Koegel Brunnian Clothes on the Runway: Not for
the Bashful . . . . . . . . . . . . . . 741--748
Ehud Friedgut Hypergraphs, Entropy, and Inequalities 749--760
Skip Garibaldi The Characteristic Polynomial and
Determinant Are Not Ad Hoc Constructions 761--778
Marc Frantz How Conics Govern Möbius Transformations 779--790
Warren P. Johnson How Cauchy Missed Ramanujan's $_1
\psi_1$ Summation . . . . . . . . . . . 791--800
Jan van Mill A Note on the Effros Theorem . . . . . . 801--806
Song Heng Chan An Elementary Proof of Jacobi's Six
Squares Theorem . . . . . . . . . . . . 806--811
Nils R. Barth Computing Cavalieri's Quadrature Formula
by a Symmetry of the $n$-Cube . . . . . 811--813
Deniz Kazanci and
Andrew Vince A Property of Normal Tilings . . . . . . 813--816
Andrzej Nowojewski and
Jakub Kallas and
Andrzej Dragan and
Abe Shenitzer and
Stefan Mykytiuk and
John Stillwell On the Appearance of Moving Bodies . . . 817--821
Marius Ghergu Problem 11110 . . . . . . . . . . . . . 822--822
Pál Péter Dalyay Problem 11111 . . . . . . . . . . . . . 822--822
Yongge Tian Problem 11112 . . . . . . . . . . . . . 822--822
Isaac Sofair Problem 11113 . . . . . . . . . . . . . 822--822
Benne de Weger Problem 11114 . . . . . . . . . . . . . 823--823
Jack Clark Problem 11115 . . . . . . . . . . . . . 823--823
Darko Veljan Problem 11116 . . . . . . . . . . . . . 823--823
Ye Zhong Hao and
Wu Wei Chao and
J. Schaer Gossard Perspector: 10980 . . . . . . . 823--824
Roland Bacher and
Julio Kuplinsky and
Richard Stong A Family of Polynomials: 10989 . . . . . 824--825
Rick Mabry and
Bernardo M. Ábrego The Envelope, Please: 10990 . . . . . . 825--826
Raymond Mortini and
S. Amghibech A Nonholomorphic Map of the Disk: 10991 826--827
David Lubell and
Chris Hill and
Albert Nijenhuis Equal Sums of Reciprocal Products: 10992 827--829
David Savitt and
Chris Hill Recognizing $n$-Divergent Sequences:
10994 . . . . . . . . . . . . . . . . . 829--829
Louis H. Kauffman Book Review: \booktitle[untitled] . . . 830--838
Anonymous Back Matter . . . . . . . . . . . . . . 839--840
Anonymous Front Matter . . . . . . . . . . . . . . ??
Judith V. Grabiner Newton, Maclaurin, and the Authority of
Mathematics . . . . . . . . . . . . . . 841--852
Tom M. Apostol and
Mamikon A. Mnatsakanian Figures Circumscribing Circles . . . . . 853--863
Hartmut Logemann and
Eugene P. Ryan Asymptotic Behaviour of Nonlinear
Systems . . . . . . . . . . . . . . . . 864--889
Stephanie Edwards and
Russell A. Gordon Extreme Curvature of Polynomials . . . . 890--899
Heinrich v. Weizsäcker Can One Drop $ L^1 $-Boundedness in
Komlós's Subsequence Theorem? . . . . . . 900--903
G. D. Chakerian and
M. S. Klamkin A Three-Point Characterization of
Central Symmetry . . . . . . . . . . . . 903--905
Iosif Pinelis L'Hospital Rules for Monotonicity and
the Wilker--Anglesio Inequality . . . . 905--909
Noriaki Kimura and
Kenneth S. Williams Infinitely Many Insolvable Diophantine
Equations . . . . . . . . . . . . . . . 909--913
Jón R. Stefánsson Forward Shifts and Backward Shifts in a
Rearrangement of a Conditionally
Convergent Series . . . . . . . . . . . 913--914
Michael Nyblom Problem 11117 . . . . . . . . . . . . . 915--915
Vesselin Dimitrov Problem 11118 . . . . . . . . . . . . . 915--915
John Robertson Problem 11119 . . . . . . . . . . . . . 915--915
Bob Berk and
Larry Shepp Problem 11120 . . . . . . . . . . . . . 915--915
H. A. ShahAli Problem 11121 . . . . . . . . . . . . . 916--916
Victor Pambuccian Problem 11122 . . . . . . . . . . . . . 916--916
Art\=uras Dubickas Problem 11123 . . . . . . . . . . . . . 916--916
Giorgi Goldoni and
Alan Berele An Excenteric Iteration: 10993 . . . . . 916--917
Donato Trigiante and
Albert Stadler Where Are the Zeros?: 10995 . . . . . . 917--917
Ed T. Prothro and
Chris Hill Prime Divisors of Fermat Numbers: 10997 917--918
Roberto Tauraso and
Jiri Lebl Distance to the Boundary: 10998 . . . . 918--918
George Lamb and
Cornelius Stallmann and
Gerald Thompson and
Zafar Ahmed and
O. P. Lossers An Integral Three Ways: 11000 . . . . . 918--920
Rick Mabry and
Jody Lockhart Powered Terms in a Series: 11001 . . . . 920--920
Y.-F. S. Pétermann and
C. T. Stretch and
Jamie Simpson A Problem That Bears Repeating: 11002 920--921
Stephen B. Gray and
Clayton W. Dodge The Orthocenter and Circumcenter Are
Isogonal Conjugate Points: 11003 . . . . 921--922
Anonymous Errata for 2004: 11089 . . . . . . . . . 922--922
Anonymous Errata for 2004: Fibonacci in Complex
Camouflage: 10858 . . . . . . . . . . . 922--922
Anonymous Errata for 2004: a Group Determined by
Relations?: 10933 . . . . . . . . . . . 922--922
Anonymous Errata for 2004: An Iterative Sequence:
10988 . . . . . . . . . . . . . . . . . 922--922
Anonymous Errata for 2004: Some Bernstein
Polynomials: 10985 . . . . . . . . . . . 922--922
Philip Protter Book Review: \booktitle[untitled] . . . 923--926
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 927--929
Anonymous Volume Information . . . . . . . . . . . 930--937
Anonymous Back Matter . . . . . . . . . . . . . . 938--944
Anonymous Front Matter . . . . . . . . . . . . . . ??
William Dunham Touring the Calculus Gallery . . . . . . 1--19
Marcel Wild The Groups of Order Sixteen Made Easy 20--31
Shif Berhanu and
Ahmed Mohammed A Harnack Inequality for Ordinary
Differential Equations . . . . . . . . . 32--41
Janko Hernández and
Leonel Robert Figures of Constant Width on a
Chessboard . . . . . . . . . . . . . . . 42--50
H. S. Bear and
Dale Myers A Simpler Approach to Integration and
the Fubini Theorem . . . . . . . . . . . 51--60
Jonathan Sondow Double Integrals for Euler's Constant
and in $ \ln (4 / \pi) $ and an Analog
of Hadjicostas's Formula . . . . . . . . 61--65
Dan Romik Roots of the Derivative of a Polynomial 66--69
Joel L. Weiner and
George R. Wilkens Quaternions and Rotations in $ \mathbb
{E}^4 $ . . . . . . . . . . . . . . . . 69--76
José Carlos de Sousa and
Oliveira Santos Another Proof of the Fundamental Theorem
of Algebra . . . . . . . . . . . . . . . 76--78
V. F. Kagan Riemann's Geometric Ideas . . . . . . . 79--86
Bogdan Nica Problem 11124 . . . . . . . . . . . . . 87--87
Shahin Amrahov Problem 11125 . . . . . . . . . . . . . 87--87
James S. Weber Problem 11126 . . . . . . . . . . . . . 87--87
Li Zhou Problem 11127 . . . . . . . . . . . . . 87--87
Wu Wei Chao and
O. P. Lossers Point Causing Equal Angles: 10996 . . . 88--88
Tom Apostol Problem 11128 . . . . . . . . . . . . . 88--88
Yongge Tian Problem 11129 . . . . . . . . . . . . . 88--88
Paul Bateman Problem 11130 . . . . . . . . . . . . . 88--88
Victor Pambuccian and
Michael Wolterman Saccheri Quadrilateral: 11004 . . . . . 88--89
Marty Getz and
Dixon Jones and
Ken Dutch Partitioning by Arithmetic Progressions:
11005 . . . . . . . . . . . . . . . . . 89--90
Bogdan Suceav\ua and
Daniele Donini A Circle Centered on the Euler Circle:
11006 . . . . . . . . . . . . . . . . . 90--91
José Luis Díaz-Barrero and
Juan José Egozcue and
Art\=uras Dubickas Zero and Coefficient Inequality: 11008 91--92
David Borwein and
Julien Grivaux Convex and Concave Functions: 11009 . . 92--93
Erwin Just and
Norman Schaumberger and
GCHQ Problem Solving Group Regular Polygon Inscription: 11010 . . . 93--94
Steve Kennedy Book Review: \booktitleTuring: A Novel
About Computation, by Christos H.
Papadimitriou . . . . . . . . . . . . . 95--98
Marion D. Cohen Book Review: \booktitleThe Magic of
Numbers, by Benedict Gross; Joe Harris 98--101
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Gregory S. Warrington Juggling Probabilities . . . . . . . . . 105--118
Alex D. D. Craik Prehistory of Fa\`a di Bruno's Formula 119--130
Paolo Codec\`a and
Mohan Nair The Lesser-Known $ \Delta $-Function in
Number Theory . . . . . . . . . . . . . 131--140
Juan Carlos Álvarez Paiva and
Anthony Thompson On the Perimeter and Area of the Unit
Disc . . . . . . . . . . . . . . . . . . 141--154
Ian Doust and
Michael D. Hirschhorn and
Jocelyn Ho Trigonometric Identities, Linear
Algebra, and Computer Algebra . . . . . 155--164
Connie Campbell and
William Staton A Square-Packing Problem of Erd\Hos . . 165--167
Laurei\ctiu Panaitopol On the Representation of Natural Numbers
as Sums of Squares . . . . . . . . . . . 168--171
Jiu Ding and
Temple H. Fay The Perron--Frobenius Theorem and Limits
in Geometry . . . . . . . . . . . . . . 171--175
Piotr Haj\lasz and
Pawe\l Strzelecki How to Measure Volume with a Thread . . 176--179
N. G. de Bruijn Problem 11131 . . . . . . . . . . . . . 180--180
Jonathan Sondow Problem 11132 . . . . . . . . . . . . . 180--180
Paul Bracken Problem 11133 . . . . . . . . . . . . . 180--180
Kent D. Boklan Problem 11134 . . . . . . . . . . . . . 180--180
Ray Redheffer Problem 11135 . . . . . . . . . . . . . 181--181
Raymond Mortini Problem 11136 . . . . . . . . . . . . . 181--181
Vicen\ctiu R\uadulescu Problem 11137 . . . . . . . . . . . . . 181--181
D. P. Minassian Baire Class One: 10999 . . . . . . . . . 181--182
George Lamb and
Zafar Ahmed An Application of the Gaussian Integral:
11011 . . . . . . . . . . . . . . . . . 182--183
C\ualin Popescu and
Chu Wenchang Cube Sum Inequalities: 11012 . . . . . . 183--184
David Callan and
Marc Renault Dyck Paths Skipping Every Fourth Point:
11013 . . . . . . . . . . . . . . . . . 184--184
Achilleas Sinefakopoulos and
Knut Dale A Recursively Defined Series: 11014 . . 184--185
Ovidiu Furdui and
Li Zhou Sines in a Triangle: 11015 . . . . . . . 185--186
C. R. Pranesachar and
S. Amghibech When the Brocard Points Are Collinear
with a Vertex: 11017 . . . . . . . . . . 186--187
Eric S. Weber Book Review: \booktitleAn Introduction
to Frames and Riesz Bases, by Ole
Christensen . . . . . . . . . . . . . . 188--191
Jeffrey L. Nunemacher Book Review: \booktitleGeometry, by
David A. Brannan; Matthew F. Esplen;
Jeremy J. Gray . . . . . . . . . . . . . 191--194
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front matter . . . . . . . . . . . . . . ??
Robert E. Megginson Yueh-Gin Gung and Dr. Charles Y. Hu
Award to Gerald L. Alexanderson for
Distinguished Service to Mathematics . . 197--199
Roger C. Alperin Trisections and Totally Real Origami . . 200--211
John Bryk and
Cesar E. Silva Measurable Dynamics of Simple $p$-adic
Polynomials . . . . . . . . . . . . . . 212--232
Ivor Grattan-Guinness The ``Ecole Polytechnique'', 1794-1850:
Differences over Educational Purpose and
Teaching Practice . . . . . . . . . . . 233--250
William Duke and
Kimberly Hopkins Quadratic Reciprocity in a Finite Group 251--256
Shay Gueron and
Itai Shafrir A Weighted Erd\Hos--Mordell Inequality
for Polygons . . . . . . . . . . . . . . 257--263
Luo Xuebo and
Zhu-Jun Zheng An Inequality for Homogeneous
Polynomials on $ \mathbb {R}^n $ . . . . 264--266
Peter G. Anderson and
Arthur T. Benjamin and
Jeremy A. Rouse Combinatorial Proofs of Fermat's,
Lucas's, and Wilson's Theorems . . . . . 266--268
Kurt Girstmair On an Irreducibility Criterion of M. Ram
Murty . . . . . . . . . . . . . . . . . 269--270
Robert J. MacG. Dawson On a ``Singular'' Integration Technique
of Poisson . . . . . . . . . . . . . . . 270--272
Roberto Tauraso Problem 11138 . . . . . . . . . . . . . 273--273
Grahame Bennett Problem 11139 . . . . . . . . . . . . . 273--273
Walther Janous Problem 11140 . . . . . . . . . . . . . 273--273
Richard Bagby Problem 11141 . . . . . . . . . . . . . 273--273
Donald Knuth Problem 11142 . . . . . . . . . . . . . 273--274
Alexander Dubinov and
Irina Dubinova Problem 11143 . . . . . . . . . . . . . 274--274
Ernst Schulte-Geers Problem 11144 . . . . . . . . . . . . . 274--274
Joel Zinn Problem 11076 . . . . . . . . . . . . . 274--274
Bob Berk and
Larry Shepp Problem 11120 . . . . . . . . . . . . . 274--274
Art\=uras Dubickas Problem 11123 . . . . . . . . . . . . . 274--274
Slavko Simic and
Richard Stong Entire Functions of Order Zero: 11018 274--277
Bernardo Recamán Santos and
Michail Reid and
Kevin Ford Cycling via Common Divisors: 11019 . . . 277--278
Donald Knuth and
Silvia Fernández and
Gerry Myerson A Modular Triple: 11021 . . . . . . . . 279--280
Wu Wei Chao and
Nadjib Bouzar and
Allan K. Swett A Timely Problem: 11023 . . . . . . . . 280--280
Razvan Satnoianu and
Walther Janous A Two-Triangle Inequality: 11022 . . . . 280--280
Gerald B. Folland and
Jeffrey L. Stuart Book Review: \booktitleLinear Algebra,
by John B. Fraleigh; Raymond A.
Beauregard; Linear Algebra and its
Applications ~by David Lay; Linear
Algebra: A Geometric Approach ~by
Theodore Shifrin; Malcolm R. Adams;
Introduction to Linear Algebra ~by
Gilbert Strang . . . . . . . . . . . . . 281--288
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Don Shimamoto and
Catherine Vanderwaart Spaces of Polygons in the Plane and
Morse Theory . . . . . . . . . . . . . . 289--310
Edward B. Burger A Tail of Two Palindromes . . . . . . . 311--321
Sherman Stein Remarks on the Gravity Equation . . . . 322--333
Christopher S. Simons An Elementary Approach to the Monster 334--341
Daniel J. Velleman The Generalized Simpson's Rule . . . . . 342--350
Boris Mirman Sufficient Conditions for Poncelet
Polygons Not to Close . . . . . . . . . 351--356
Jürgen Kindler A Simple Proof of Sion's Minimax Theorem 356--358
John Clifford and
David James and
Michael Lachance and
Joan Remski A Constructive Approach to Singular
Value Decomposition and Symmetric Schur
Factorization . . . . . . . . . . . . . 358--363
Marco Dall'Aglio and
Fabio Maccheroni Fair Division without Additivity . . . . 363--365
Joel Zinn Problem 11145 . . . . . . . . . . . . . 366--366
Yongge Tian Problem 11146 . . . . . . . . . . . . . 366--366
Pamela Gorkin Problem 11147 . . . . . . . . . . . . . 366--366
M. L. Glasser Problem 11148 . . . . . . . . . . . . . 366--366
Mircea Ivan and
Ioan Rasa Problem 11149 . . . . . . . . . . . . . 367--367
Emeric Deutsch Problem 11150 . . . . . . . . . . . . . 367--367
Donald Knuth Problem 11151 . . . . . . . . . . . . . 367--367
Jonathan Sondow and
Richard Stong and
Julien Grivaux An Identity Involving Harmonic Numbers:
11026 . . . . . . . . . . . . . . . . . 367--369
H. Reuvers and
Li Zhou and
A. Engle Triangles Inscribed in a Circle: 11027 369--370
Götz Trenkler and
G. P. Shannon Hermitian Products of Hermitian
Matrices: 11028 . . . . . . . . . . . . 370--371
Steven Butler and
Bruce Ebanks A Functional Equation: 11030 . . . . . . 371--372
Li Zhou and
Robin Chapman Monster Mean Tamed: 11031 . . . . . . . 372--373
David E. Rowe Book Review: \booktitleMathematicians
under the Nazis, by Sanford L. Segal . . 374--381
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front matter . . . . . . . . . . . . . . ??
Arturo Magidin and
David McKinnon Gauss's Lemma for Number Fields . . . . 385--416
Florian Deloup The Fundamental Group of the Circle Is
Trivial . . . . . . . . . . . . . . . . 417--425
Antonio Behn and
Christopher Kribs-Zaleta and
Vadim Ponomarenko The Convergence of Difference Boxes . . 426--439
Paul E. Becker Do Normal Subgroups Have Straight Tails? 440--449
Raghib Abu-Saris and
Wajdi Ahmad Avoiding Eigenvalues in Computing Matrix
Powers . . . . . . . . . . . . . . . . . 450--454
Francesc Comellas and
J. Luis A. Yebra Exact Solutions for Minimax Optimization
Problems . . . . . . . . . . . . . . . . 454--458
F. G. Avkhadiev A Simple Proof of the Gauss-Winckler
Inequality . . . . . . . . . . . . . . . 459--462
Mowaffaq Hajja Copositive Symmetric Cubic Forms . . . . 462--466
Mircea Ivan Problem 11152 . . . . . . . . . . . . . 467--467
Paul Bracken Problem 11153 . . . . . . . . . . . . . 467--467
Kent Holing Problem 11154 . . . . . . . . . . . . . 467--467
Emmanuel Kowalski Problem 11155 . . . . . . . . . . . . . 467--467
Richard Stanley Problem 11156 . . . . . . . . . . . . . 467--468
Hillel Gauchman Problem 11157 . . . . . . . . . . . . . 468--468
David Beckwith Problem 11158 . . . . . . . . . . . . . 468--468
Juan-Bosco Romero Márquez and
Martin Muldoon Gamma Function Bounds: 11016 . . . . . . 468--468
Tim Keller and
Doyle Henderson One Good Factorization Deserves Another:
11029 . . . . . . . . . . . . . . . . . 469--469
Mark Pinsky and
Nicholas Singer The Stationary Distribution of a
Tridiagonal Row-Stochastic Matrix: 11032 469--470
M. N. Deshpande and
R. M. Welukar and
Richard Stong and
BSI Problems Group Expansion by Inclusion-Exclusion: 11033 470--472
Omer Yayenie and
Joe Geiman Evaluation of an Integral: 11035 . . . . 472--473
M. L. J. Hautus and
Julien Grivaux Shrinking Fréchet Differentiable Maps:
11037 . . . . . . . . . . . . . . . . . 473--474
Floor van Lamoen and
Michel Bataille Morley's Triangle and Lemma: 11038 . . . 474--474
Daniel J. Madden Book Review: \booktitleAbstract Algebra,
by Ronald Solomon; Integers, Polynomials
and Rings ~by Ronald S. Irving . . . . . 475--478
John Sylvester Book Review: \booktitleIntroduction to
the Mathematics of Medical Imaging, by
Charles L. Epstein . . . . . . . . . . . 479--480
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Arthur T. Benjamin and
Naiomi T. Cameron Counting on Determinants . . . . . . . . 481--492
Jonathan Michael Borwein and
Kwok-Kwong Stephen Choi and
Wilfried Pigulla Continued Fractions of Tails of
Hypergeometric Series . . . . . . . . . 493--501
Michel Balinski What Is Just? . . . . . . . . . . . . . 502--511
Nathaniel Grossman A $ C^\infty $ Lagrange Inversion
Theorem . . . . . . . . . . . . . . . . 512--514
Mark A. Pinsky Mean Values and the Maximum Principle: a
Proof in Search of More Theorems . . . . 515--521
H. Maehara and
T. Zamfirescu On the Perimeter of a Triangle in a
Minkowski Plane . . . . . . . . . . . . 521--522
Daniel Frohn A (K)-Ring Satisfying the Ascending
Chain Condition on Principal Ideals That
Is Not a Principal Ideal Ring . . . . . 523--524
Lee Lorch Continuous Ranking of Zeros of Cylinder
Functions . . . . . . . . . . . . . . . 524--525
Viktor Blåsjö The Isoperimetric Problem . . . . . . . 526--566
George Lamb Problem 11159 . . . . . . . . . . . . . 567--567
Marc Chamberland Problem 11160 . . . . . . . . . . . . . 567--567
Emeric Deutsch Problem 11161 . . . . . . . . . . . . . 567--567
Paolo Perfetti Problem 11162 . . . . . . . . . . . . . 567--567
Michel Bataille Problem 11163 . . . . . . . . . . . . . 567--567
Luis Díaz-Barrero Problem 11164 . . . . . . . . . . . . . 568--568
Yogesh More Problem 11165 . . . . . . . . . . . . . 568--568
William P. Wardlaw and
Richard Stong Adjoint over the Smallest Field: 11034 568--569
M. L. Glasser and
George Lamb One Easy, One Hard: 11036 . . . . . . . 569--572
Noah Rosenberg and
Richard Bagby Integral over a Simplex: 11039 . . . . . 572--573
Yongge Tian and
BSI Problems Group Range Identities for Hermitian
Idempotent Matrices: 11040 . . . . . . . 573--573
M. N. Deshpande and
John Henry Steelman An Invariance of Variance over
Expectation: 11042 . . . . . . . . . . . 573--574
D. J. H. Garling Book Review: \booktitleThe
Cauchy--Schwarz Master Class: An
Introduction to the Art of Mathematical
Inequalities, by J. Michael Steele . . . 575--579
Loukas Grafakos Book Review: \booktitleConstantin
Carathéodory: Mathematics and Politics in
Turbulent Times, by Maria Georgiadou . . 579--581
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Kang-Tae Kim and
Steven G. Krantz The Automorphism Groups of Domains . . . 585--601
Greg Dresden and
Wayne M. Dym\`a\vcek Finding Factors of Factor Rings over the
Gaussian Integers . . . . . . . . . . . 602--611
Dov Aharonov and
Alan Beardon and
Kathy Driver Fibonacci, Chebyshev, and Orthogonal
Polynomials . . . . . . . . . . . . . . 612--630
Stephen T. Ahearn Tolstoy's Integration Metaphor from War
and Peace . . . . . . . . . . . . . . . 631--638
Mark Finkelstein and
Robert Whitley Eigenvalues, Almost Periodic Functions,
and the Derivative of an Integral . . . 639--641
J. Araújo and
J. D. Mitchell An Elementary Proof That Every Singular
Matrix Is a Product of Idempotent
Matrices . . . . . . . . . . . . . . . . 641--645
Michael J. Grady A Group Theoretic Approach to a Famous
Partition Formula . . . . . . . . . . . 645--651
David A. Ross An Elementary Proof of Lyapunov's
Theorem . . . . . . . . . . . . . . . . 651--653
Greg Oman Problem 11166 . . . . . . . . . . . . . 654--654
Vicen\ctiu R\uadulescu Problem 11167 . . . . . . . . . . . . . 654--654
Kent Holing Problem 11168 . . . . . . . . . . . . . 654--654
Mohammad Hossein Mehrabi Problem 11169 . . . . . . . . . . . . . 654--654
Emeric Deutsch Problem 11170 . . . . . . . . . . . . . 655--655
Chu Cheng Problem 11171 . . . . . . . . . . . . . 655--655
Heinz-Jürgen Seiffert Problem 11172 . . . . . . . . . . . . . 655--655
Oscar Ciaurri and
Florin Boca Hyperbolic-Looking Special Functions:
11041 . . . . . . . . . . . . . . . . . 655--657
Michael Golomb Don't the Problem Ebitees Read the
Monthly? 11043 . . . . . . . . . . . . . 657--657
Michel Bataille and
Li Zhou A Combinatorial Sum Goes on Tangent:
11044 . . . . . . . . . . . . . . . . . 657--659
Matthias Beck and
Marcin Mazur and
Shelemyahu Zacks ``Ordinary'' Spherical Triangles: 11048 659--660
Vasile Mihai and
Zoltán V\Hor\Hos One of the Morley Triangles: 11049 . . . 660--661
Wu Wei Chao and
The University of Louisiana at Lafayette Math Club Two Functional Equations: 11053 . . . . 661--662
Razvan Satnoianu and
Daniele Donini Medians and Altitudes and the Sum of the
Radii: 11055 . . . . . . . . . . . . . . 662--663
Kenneth B. Stolarsky Book Review: \booktitleAnalytic Theory
of Polynomials, by Qazi Ibadur Rahman;
Gerhard Schmeisser; Complex Polynomials
~by Terry Sheil-Small . . . . . . . . . 664--671
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front matter . . . . . . . . . . . . . . ??
Karl Dilcher and
Kenneth B. Stolarsky A Pascal-Type Triangle Characterizing
Twin Primes . . . . . . . . . . . . . . 673--681
David A. Cox and
Jerry Shurman Geometry and Number Theory on Clovers 682--704
George Leibman A Nonstandard Proof of the Fundamental
Theorem of Algebra . . . . . . . . . . . 705--712
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-Fifth William Lowell Putnam
Mathematical Competition . . . . . . . . 713--725
N. V. Rao The Stone--Weierstrass Theorem Revisited 726--729
Jonathan Sondow A Faster Product for $ \pi $ and a New
Integral for $ \ln \pi / 2 $ . . . . . . 729--734
I. M. Isaacs and
M. R. Pournaki Generalizations of Fermat's Little
Theorem via Group Theory . . . . . . . . 734--740
Geoffrey Brown Convexity and Minkowski's Inequality . . 740--742
B. A. Rosenfeld The Analytic Principle of Continuity . . 743--748
M. N. Deshpande Problem 11173 . . . . . . . . . . . . . 749--749
Pál Péter Dályay Problem 11174 . . . . . . . . . . . . . 749--749
William Calbeck Problem 11175 . . . . . . . . . . . . . 749--749
Oleg Faynshteyn Problem 11176 . . . . . . . . . . . . . 749--749
Dorin M\uarghidanu Problem 11177 . . . . . . . . . . . . . 750--750
Jon Bentley and
Colin Mallows Problem 11178 . . . . . . . . . . . . . 750--750
David Beckwith Problem 11179 . . . . . . . . . . . . . 750--750
Manoj Prakash Singh and
Richard Stong A Prime Summandification of n: 11045 . . 750--751
Shahin Amrabov and
Bernard M. Abrego An Application of Fermat's Little
Theorem: 11054 . . . . . . . . . . . . . 751--751
Syrous Marivani and
O. P. Lossers Modular Sequences Defined by
Polynomials: 11047 . . . . . . . . . . . 751--751
John H. Lindsey II and
Omran Kouba Maximum Compared to Average: 11056 . . . 752--752
Óscar Ciaurri and
O. P. Lossers A Vanishing Infinite Sum: 11058 . . . . 752--753
Matthew Coppenbarger and
GCHQ Problem Solving Group ``Little Boxes Made of Ticky-Tacky'':
11060 . . . . . . . . . . . . . . . . . 753--754
Kenneth Schilling and
BSI Problems Group Powered Divergence: 11062 . . . . . . . 754--755
John Wetzel and
Li Zhou Lengths of Wrapped Curves: 11064 . . . . 755--755
Douglas B. Tyler and
Robin Chapman A More General Presentation: 11065 . . . 755--756
Judith Grabiner Book Review: \booktitleFrom Newton to
Hawking: A History of Cambridge
University's Lucasian Professors of
Mathematics, by Kevin C. Knox; Richard
Noakes . . . . . . . . . . . . . . . . . 757--762
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Ibtesam Bajunaid and
Joel M. Cohen and
Flavia Colonna and
David Singman Function Series, Catalan Numbers, and
Random Walks on Trees . . . . . . . . . 765--785
Dan Kalman Virtual Empirical Investigation: Concept
Formation and Theory Justification . . . 786--798
Nikolai V. Ivanov A Differential Forms Perspective on the
Lax Proof of the Change of Variables
Formula . . . . . . . . . . . . . . . . 799--806
Roger C. Alperin The Modular Tree of Pythagoras . . . . . 807--816
Ray Redheffer The Behavior of Solutions near a Stable
or Semistable Stationary Point . . . . . 817--822
M. A. Nyblom More Nested Square Roots of 2 . . . . . 822--825
A. R. Naghipour A Simple Proof of Cohen's Theorem . . . 825--826
Thierry Coquand and
Henri Lombardi A Short Proof for the Krull Dimension of
a Polynomial Ring . . . . . . . . . . . 826--829
Robert Myers An Elementary Proof of Joris's Theorem 829--831
Michael Monastyrsky Some Remarks on ``Mathematics at the
Tlirn of the Millennium'' . . . . . . . 832--838
Suat Namli Problem 11180 . . . . . . . . . . . . . 839--839
M. N. Deshpande Problem 11181 . . . . . . . . . . . . . 839--839
Shahin Amrahov Problem 11182 . . . . . . . . . . . . . 839--839
David Beckwith Problem 11183 . . . . . . . . . . . . . 839--839
Slavko Simic Problem 11184 . . . . . . . . . . . . . 840--840
Rainer Brück Problem 11185 . . . . . . . . . . . . . 840--840
Angelo J. Christino, Jr. and
William C. Waterhouse Problem 11186 . . . . . . . . . . . . . 840--840
Kent Holing and
Richard Stong A Special Set of Integer Points in
Space: 11050 . . . . . . . . . . . . . . 840--841
Slavko Simic and
John H. Lindsey II Equivalent Asymptotics: 11063 . . . . . 841--843
George Lamb and
O. P. Lossers Integral by Mellin Transform: 11067 . . 843--844
Herbert S. Wilf and
Kenneth E. Schilling Think Rationally: 11068 . . . . . . . . 844--845
George Lamb and
T. K. Callahan Evaluate an Integral: 11072 . . . . . . 845--846
J. David Logan Book Review: \booktitleMathematical
Models in Biology, by Elizabeth S.
Allman; John A. Rhodes . . . . . . . . . 847--850
Virginia M. Warfield Book Review: \booktitleCount Down: Six
Kids Vie for Glory at the World's
Toughest Math Competition, by Steve
Olson . . . . . . . . . . . . . . . . . 850--851
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Lisa D. Humphreys and
P. Joseph McKenna When a Mechanical Model Goes Nonlinear:
Unexpected Responses to Low-Periodic
Shaking . . . . . . . . . . . . . . . . 861--875
Eric Driver and
Philip A. Leonard and
Kenneth S. Williams Irreducible Quartic Polynomials with
Factorizations modulo p . . . . . . . . 876--890
Stephen M. Zemyan On the Zeroes of the Nth Partial Sum of
the Exponential Series . . . . . . . . . 891--909
Jan J. Dijkstra On Homeomorphism Groups and the
Compact-Open Topology . . . . . . . . . 910--912
Zhibo Chen and
Gary L. Mullen Transpositions and Representability . . 913--919
Oleg Pikhurko Generating Edge-Labeled Trees . . . . . 919--921
Adrian Dumitrescu A Remark on the Erd\Hos--Szekeres
Theorem . . . . . . . . . . . . . . . . 921--924
Seon-Hong Kim On the Moduli of the Zeros of a
Polynomial . . . . . . . . . . . . . . . 924--925
Leif Arkeryd Nonstandard Analysis . . . . . . . . . . 926--928
Li Zhou Problem 11187 . . . . . . . . . . . . . 929--929
David Bailey Problem 11188 . . . . . . . . . . . . . 929--929
Lajos Csete Problem 11189 . . . . . . . . . . . . . 929--929
José Luis Díaz-Barrero Problem 11190 . . . . . . . . . . . . . 929--929
Barthel Wayne Huff Problem 11191 . . . . . . . . . . . . . 929--930
Brett Stevens Problem 11192 . . . . . . . . . . . . . 930--930
Marian Tetiva Problem 11193 . . . . . . . . . . . . . 930--930
Floor van Lamoen Six Surprises from Four Lines: 11025 . . 930--932
Sebastian Cioab\ua and
Tim LeSaulnier and
Dan Saracino A Sufficient Condition for
Commutativity: 11066 . . . . . . . . . . 932--933
Péter Ivády and
Richard Stong Sine Bound: 11069 . . . . . . . . . . . 933--933
Götz Trenkler and
Lawrence J. Baker An Easy Complex Inequality: 11075 . . . 933--933
Gheorge Costovici and
Uro\vs Milutinovi\'c An Oscillating Sequence: 11077 . . . . . 934--934
Razvan Satnoianu and
Li Zhou A Majorization Consequence: 11080 . . . 934--935
Stephen Morse and
Robin Chapman Harmonious Trios Are the Vertices of a
Regular Icosahedron: 11081 . . . . . . . 935--935
Wu Wei Chao Errata: Continuous Additive Functions 936--936
Marty Getz and
Dixon Jones Errata: Partitioning by Arithmetic
Progressions . . . . . . . . . . . . . . 936--936
Michael Golomb and
Kit Hanes The Orthocenter of a Simplex: 11087 . . 936--936
Gerald B. Folland Book Review: \booktitleFunctional
Analysis, by Peter D. Lax; John Wiley;
Functional Analysis: An Introduction ~by
Yuli Eidelman; Vitaly Milman; Antonis
Tsolomitis . . . . . . . . . . . . . . . 937--940
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 941--946
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Anonymous Volume Information . . . . . . . . . . . ??
Andrew Granville and
Greg Martin Prime Number Races . . . . . . . . . . . 1--33
John W. Hagood and
Brian S. Thomson Recovering a Function from a Dini
Derivative . . . . . . . . . . . . . . . 34--46
Marc Frantz Some Graphical Solutions of the Kepler
Problem . . . . . . . . . . . . . . . . 47--56
Henry Cohn A Short Proof of the Simple Continued
Fraction Expansion of $e$ . . . . . . . 57--62
Thomas J. Osler A Proof of the Continued Fraction
Expansion of $e$1/M . . . . . . . . . . 62--66
Xiongping Dai Continuous Differentiablity of Solutions
of ODEs with Respect to Initial
Conditions . . . . . . . . . . . . . . . 66--70
Stephen Boyd and
Persi Diaconis and
Jun Sun and
Lin Xiao Fastest Mixing Markov Chain on a Path 70--74
Pawe\l Strzelecki and
Abe Shenitzer The Poincaré Conjecture? . . . . . . . . 75--78
Folkmar Bornemann Problem 11194 . . . . . . . . . . . . . 79--79
Marian Tetiva Problem 11195 . . . . . . . . . . . . . 79--79
Mohammad Hossein Mehrabi Problem 11196 . . . . . . . . . . . . . 79--79
Oleg Faynshteyn Problem 11197 . . . . . . . . . . . . . 79--79
P. R. Parthasarathy Problem 11198 . . . . . . . . . . . . . 79--79
Aliyev Yakub Problem 11199 . . . . . . . . . . . . . 80--80
Joel Zinn Problem 11200 . . . . . . . . . . . . . 80--80
A. J. Sasane and
Robin Chapman Diagonals of a Regular Polygon: 10924 80--81
Nick MacKinnon and
Kenneth Schilling Optimal Strategy for a Number-Guessing
Game: 11051 . . . . . . . . . . . . . . 81--82
Zahlreich Problems Group and
C. T. Stretch A Point with Given Distances: 11057 . . 82--83
Mark Bowron and
Bruce Burdick Closure, Complement, and Union: 11059 83--83
Roberto Tauraso and
Richard Stong Commuting Analytic Maps: 11070 . . . . . 83--84
Matthias Beck and
Jesus DeLoera and
Mike Develin and
Julian Pfeifle and
Northwestern University Math Problem Solving Group Some Linear Recurrences: 11085 . . . . . 84--85
Richard Holzsager and
Anton R. Schep Rearranged Series: 11088 . . . . . . . . 85--85
Michel Bataille and
O. P. Lossers Simple Roots for Polynomials: 11094 . . 85--86
Charles Radin Book Review: \booktitleThe Pursuit of
Perfect Packing, by Tomaso Aste; Denis
Weaire; Kelper's Conjecture ~by George
G. Szpiro . . . . . . . . . . . . . . . 87--90
Shandelle M. Henson Book Review: \booktitleComplexities:
Women in Mathematics, by Bettye Anne
Case; Anne M. Leggett . . . . . . . . . 91--93
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Jeffrey C. Lagarias Wild and Wooley Numbers . . . . . . . . 97--108
Alejo Blaya and
Víctor Jiménez López Is Trivial Dynamics That Trivial? . . . 109--133
Vladimir Pozdnyakov and
Martin Kulldorff Waiting Times for Patterns and a Method
of Gambling Teams . . . . . . . . . . . 134--143
Louis A. Talman Simpson's Rule Is Exact for Quintics . . 144--155
Herbert A. Medina A Sequence of Polynomials for
Approximating Arctangent . . . . . . . . 156--161
Reinhard Diestel and
Carsten Thomassen A Cantor--Bernstein Theorem for Paths in
Graphs . . . . . . . . . . . . . . . . . 161--165
John Konvalina and
Jack Heidel and
Jim Rogers A Mean Paradox . . . . . . . . . . . . . 166--169
Enrique Arrondo Another Elementary Proof of the
Nullstellensatz . . . . . . . . . . . . 169--171
P. L. Robinson The Sphere Is Not Flat . . . . . . . . . 171--173
Daniel J. Velleman A Note on $ \lambda $-Permutations . . . 173--178
Robert Russell Problem 11201 . . . . . . . . . . . . . 179--179
Grahame Bennett Problem 11202 . . . . . . . . . . . . . 179--179
Fuxiang Yu Problem 11203 . . . . . . . . . . . . . 179--179
Christopher J. Hillar Problem 11204 . . . . . . . . . . . . . 179--179
Wu Wei Chao and
Guang Zhou Problem 11205 . . . . . . . . . . . . . 179--179
Mircea Ivan and
Alexandru Lupa\cs Problem 11206 . . . . . . . . . . . . . 180--180
Michael W. Botsko Problem 11207 . . . . . . . . . . . . . 180--180
Andrei Jorza and
Edward Ordman and
Richard Stong No Three Faces with the Same Number of
Edges: 10856 . . . . . . . . . . . . . . 180--183
Danrun Huang and
Daniel Scully and
Achava Nakhash and
Karl David The Limit of a Set-Valued Process: 11052 183--183
Vicen\ctiu R\vadulescu and
Richard Stong An Example With Periodic Orbits: 11073 184--186
Christopher Hillar and
Darren Rhea and
Godfrey L. Isaacs An Oldie: 11098 . . . . . . . . . . . . 186--186
David E. Zitarelli Book Review: \booktitleR. L. Moore:
Mathematician and Teacher, by John
Parker . . . . . . . . . . . . . . . . . 187--192
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Wayne Roberts Yueh-Gin Gung and Dr. Charles Y. Hu
Award to Hyman Bass for Distinguished
Service to Mathematics . . . . . . . . . 193--195
David Pengelley and
Fred Richman Did Euclid Need the Euclidean Algorithm
to Prove Unique Factorization? . . . . . 196--205
Lluís Bibiloni and
Pelegrí Viader and
Jaume Paradís On a Series of Goldbach and Euler . . . 206--220
Rajendra Bhatia Infinitely Divisible Matrices . . . . . 221--235
Harold P. Boas Reflections on the Arbelos . . . . . . . 236--249
Robert E. Hartwig Note on a Linear Difference Equation . . 250--256
Lech Maligranda Simple Norm Inequalities . . . . . . . . 256--260
Alexander Givental The Pythagorean Theorem: What Is It
About? . . . . . . . . . . . . . . . . . 261--265
YiChuan Yang A Lattice-Ordered Skew Field Is Totally
Ordered If Squares Are Positive . . . . 265--266
Li Zhou Problem 11208 . . . . . . . . . . . . . 267--267
Alexander Dubinov and
Irina Dubinova Problem 11209 . . . . . . . . . . . . . 267--267
Michael S. Becker Problem 11210 . . . . . . . . . . . . . 267--267
Mihály Bencze Problem 11211 . . . . . . . . . . . . . 268--268
David Beckwith Problem 11212 . . . . . . . . . . . . . 268--268
Stanley Rabinowitz Problem 11213 . . . . . . . . . . . . . 268--268
Solomon W. Golomb Problem 11214 . . . . . . . . . . . . . 268--268
Richard Bagby and
GCHQ Problem Solving Group Differentiable Distance: 11093 . . . . . 268--269
Vasile Mihai and
O. P. Lossers Trapezoid Inscribed in Ellipse: 11095 269--269
C\ualin Popescu and
Richard Stong A Subset-Sum Inequality: 11100 . . . . . 269--270
Earl F. Skelton and
Zoltán V\Hor\Hos An Inverse Tangent Integral: 11101 . . . 270--271
Vincent\ctiu R\vadulescu and
GCHQ Problem Solving Group Periodic Solution of a Differential
Equation: 11104 . . . . . . . . . . . . 271--273
Juan-Bosco Romero Marquez and
Rick Luttmann and
Miguel de Guzman and
G. Donald Chakerian and
Li Zhou Cevians and Centroids:11105 . . . . . . 273--274
Michel Émery and
Szeged Problem Solving Group Fejéntaláltuka A Sum Inequality:11107 . . . . . . . . . 274--274
Marius Ghergu and
Microsoft Research Problem Group Set Inclusion and Density:11110 . . . . 274--274
Michael Beeson Book Review: \booktitleA Tour through
Mathematical Logic, by Robert S. Wolf 275--280
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Óscar Martín Look-and-Say Biochemistry: Exponential
RNA and Multistranded DNA . . . . . . . 289--307
Jasbir S. Chahal Congruent Numbers and Elliptic Curves 308--317
Jeremy Gibbons Unbounded Spigot Algorithms for the
Digits of Pi . . . . . . . . . . . . . . 318--328
Bennet Vance Counting Ordered Trees by Permuting
Their Parts . . . . . . . . . . . . . . 329--335
Nils Abramson and
Jan Boman and
Björn Bonnevier Plane Intersections of Rotational
Ellipsoids . . . . . . . . . . . . . . . 336--339
Oleg Mushkarov and
Nikolai Nikolov Semiregular Polygons . . . . . . . . . . 339--344
R. B. Burckel Fubinito (Immediately) Implies FTA . . . 344--347
T. W. Körner On the Fundamental Theorem of Algebra 347--348
Paul Melvin A Topological Menagerie . . . . . . . . 348--351
Eberhard Knobloch Mathesis Perennis: Mathematics in
Ancient, Renaissance, and Modern Times 352--365
Shmuel Rosset Problem 11215 . . . . . . . . . . . . . 366--366
Ted Chinburg and
Shahriar Shahriari Problem 11216 . . . . . . . . . . . . . 366--366
Michel Bataille Problem 11217 . . . . . . . . . . . . . 366--366
Gary Gordon Problem 11218 . . . . . . . . . . . . . 366--367
R. A. Strubel Problem 11219 . . . . . . . . . . . . . 367--367
David Beckwith Problem 11220 . . . . . . . . . . . . . 367--367
Paolo Perfetti Problem 11221 . . . . . . . . . . . . . 367--367
Dimiter Skordev and
Gerry Myerson An Impossible Difference Condition:
11074 . . . . . . . . . . . . . . . . . 367--368
Donald Knuth and
Robin Chapman Cube-Free Sums: 11078 . . . . . . . . . 368--369
Brian Cook and
James Whitenton and
Richard Stong A Complex Identity: 11079 . . . . . . . 369--370
Wu Wei Chao and
National Security Agency Problems Group A Divisibility Problem: 11082 . . . . . 370--371
William P. Wardlaw and
Jean-Pierre Grivaux The Null Ideal of a Matrix: 11083 . . . 371--371
H. A. ShahAli and
Timothy LeSaulnier Finding a Repeated Difference: 11084 . . 371--372
Stephen C. Locke and
Richard Stong Coloring Graphs with Few Odd Cycles:
11086 . . . . . . . . . . . . . . . . . 372--372
Florian Luca and
John Ferdinands Sometimes $n$ Divides $ \sigma k(n) $:
11090 . . . . . . . . . . . . . . . . . 372--373
Arturo Magidin and
John Cade The Order of a Product of Group
Elements: 11092 . . . . . . . . . . . . 373--373
Paul G. Goerss Book Review: \booktitleTopology: A
Geometric Approach, by Terry Lawson . . 374--377
Carol Wood Book Review: \booktitleAlfred Tarski:
Life and Logic, by Anita Burdman
Feferman; Solomon Feferman . . . . . . . 377--379
L. Elsner Book Review: \booktitleGer\vsgorin and
His Circles, by Richard S. Varga . . . . 379--381
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Michael J. Mossinghoff A \$1 Problem . . . . . . . . . . . . . 385--402
Le Baron O. Ferguson What Can Be Approximated by Polynomials
with Integer Coefficients . . . . . . . 403--414
Marcelo Sobottka and
Luiz P. L. de Oliveira Periodicity and Predictability in
Chaotic Systems . . . . . . . . . . . . 415--424
José Antonio Adell and
Alberto Lekuona The Simplest Example of a Normal
Asymptotic Expansion . . . . . . . . . . 425--442
Mowaffaq Hajja The Arbitrariness of the Cevian Triangle 443--447
Gilbert Helmberg Curiosities concerning Weak Topology in
Hilbert Space . . . . . . . . . . . . . 447--452
Hei-Chi Chan More Formulas for $ \pi $ . . . . . . . 452--455
Detlef Gröger On Gauss's Entry from January 6, 1809 455--458
Jonathan Sondow Problem 11222 . . . . . . . . . . . . . 459--459
Christopher Hillar and
Lionel Levine Problem 11123 . . . . . . . . . . . . . 459--459
Dietrich Trenkler and
Götz Trenkler Problem 11224 . . . . . . . . . . . . . 459--459
José Luis Díaz-Barrero Problem 11225 . . . . . . . . . . . . . 459--459
Franck Beaucoup and
Tamás Erdélyi Problem 11226 . . . . . . . . . . . . . 460--460
Syrous Marivani Problem 11227 . . . . . . . . . . . . . 460--460
Marian Tetiva Problem 11228 . . . . . . . . . . . . . 460--460
Emeric Deutsch and
Marc Renault A Variation on $t$-Catalan Paths: 11071 460--461
David Callan and
GCHQ Problem Solving Group The Maximum Associativeness of Division:
11091 . . . . . . . . . . . . . . . . . 462--463
Said Amghibech and
José Heber Nieto An Application of Newton's Identities:
11096 . . . . . . . . . . . . . . . . . 463--464
Kevin Ford and
Robin Chapman Ratio of Consecutive Divisors: 11097 . . 464--464
Matthias Beck and
Richard Ehrenborg and
Thomas Zaslavsky and
Michael R. Avidon and
John H. Lindsey, II Magic Squares and Nontransitive Dice:
11099 . . . . . . . . . . . . . . . . . 464--465
Gregory Galperin and
Hillel Gauchman and
Jany C. Binz Another Summation Identity Involving
Binomial Coefficients: 11103 . . . . . . 465--466
Emeric Deutsch and
José Heber Nieto Counting Elevated Schröder Paths: 11108 466--467
Pál Péter Dalyay and
GCHQ Problem Solving Group Periodic Solution to a Functional
Equation: 11111 . . . . . . . . . . . . 467--467
Yongge Tian On the Inverse of a Product of
Orthogonal Projectors: 11112 . . . . . . 467--468
Jeffrey Nunemacher Book Review: \booktitlePrime Obsession,
by John Derbyshire; Stalking the Riemann
Hypothesis ~by Dan Rockmore . . . . . . 469--473
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
David H. Bailey and
Jonathan M. Borwein and
Vishaal Kapoor and
Eric W. Weisstein Ten Problems in Experimental Mathematics 481--509
Aaron Levin A Geometric Interpretation of an
Infinite Product for the Lemniscate
Constant . . . . . . . . . . . . . . . . 510--520
Tom M. Apostol and
Mamikon A. Mnatsakanian Solids Circumscribing Spheres . . . . . 521--540
Filip Saidak On Goldbach's Conjecture for Integer
Polynomials . . . . . . . . . . . . . . 541--545
P. Shiu Moment Sums Associated with Binary
Linear Forms . . . . . . . . . . . . . . 545--550
J. J. Koliha A Fundamental Theorem of Calculus for
Lebesgue Integration . . . . . . . . . . 551--555
Carlos D'Andrea and
Emiliano Gómez The Broken Spaghetti Noodle . . . . . . 555--557
A. F. Beardon Contractions of the Real Line . . . . . 557--558
Boris A. Kushner The Constructive Mathematics of A. A.
Markov . . . . . . . . . . . . . . . . . 559--566
Ovidiu Furdui Problem 11229 . . . . . . . . . . . . . 567--567
Gregory Keselman Problem 11230 . . . . . . . . . . . . . 567--567
Christopher Hillar Problem 11231 . . . . . . . . . . . . . 567--567
Michael W. Botsko Problem 11232 . . . . . . . . . . . . . 567--567
Robert Downes Problem 11233 . . . . . . . . . . . . . 568--568
Jim Brennan and
Richard Ehrenborg Problem 11234 . . . . . . . . . . . . . 568--568
Lenny Jones and
Rachel Keller Problem 11235 . . . . . . . . . . . . . 568--568
Stanley Rabinowitz and
Roberto Tauraso One from 1995: 10483 . . . . . . . . . . 568--569
Joel Zinn and
Gagik Amirkhanyan Related Divergent Series: 11076 . . . . 569--571
Sung Soo Kim and
C. Ray Rosentrater Another Stick-Breaking Game: 11089 . . . 571--572
Leroy Quet and
Peter Òrno A Continued Fraction Related to $ \pi $:
11102 . . . . . . . . . . . . . . . . . 572--573
Solomon W. Golomb and
Pat Costello A Consequence of Dirichlet's Theorem:
11109 . . . . . . . . . . . . . . . . . 573--573
Isaac Sofair and
Otto Ruehr Integrated by Fourier Transform: 11113 573--574
Jack Clark and
Jaime Vinuesa A Sequence Given in Terms of Harmonic
Numbers: 11115 . . . . . . . . . . . . . 574--574
Steve Kennedy Book Review: \booktitleMusings of the
Masters, by Raymond G. Ayoub . . . . . . 575--580
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
David Alan Grier Irene Stegun, the ``Handbook of
Mathematical Functions'', and the
Lingering Influence of the New Deal . . 585--597
Jon McCammond Noncrossing Partitions in Surprising
Locations . . . . . . . . . . . . . . . 598--610
Ole Christensen and
Khadija L. Christensen Linear Independence and Series
Expansions in Function Spaces . . . . . 611--627
Bernd S. W. Schröder Rearranging the Calculus Sequence to
Better Serve Its Partner Disciplines . . 628--636
Jonathan Sondow A Geometric Proof that $e$ Is Irrational
and a New Measure of Its Irrationality 637--641
Valerio De Angelis Pairings and Signed Permutations . . . . 642--644
Anupan Netyanun and
Donald C. Solmon Iterated Products of Projections in
Hilbert Space . . . . . . . . . . . . . 644--648
Danielle Silverman and
Jim Wiseman Noting the Difference: Musical Scales
and Permutations . . . . . . . . . . . . 648--651
Hao Pan On a Congruence modulo a Prime . . . . . 652--654
Jim Owings Problem 11236 . . . . . . . . . . . . . 655--655
Emeric Deutsch Problem 11237 . . . . . . . . . . . . . 655--655
Aviezri S. Fraenkel Problem 11238 . . . . . . . . . . . . . 655--655
Michel Bataille Problem 11239 . . . . . . . . . . . . . 655--655
Pál Péter Dályay Problem 11240 . . . . . . . . . . . . . 655--655
Roberto Tauraso Problem 11241 . . . . . . . . . . . . . 656--656
Gerd Herzog and
Roland Lemmert Problem 11242 . . . . . . . . . . . . . 656--656
David Callan and
Kenneth Bernstein A Lattice Path Equality: 11106 . . . . . 656--657
Darko Veljan and
Philipp Lampe Incenter Distances in a Triangulation:
11116 . . . . . . . . . . . . . . . . . 657--657
Vesselin Dimitrov and
Robin Chapman A Modular Binomial Coefficient Identity:
11118 . . . . . . . . . . . . . . . . . 657--658
John Robertson and
Microsoft Research Problems Group A Property of the Generalized Pell
Equation: 11119 . . . . . . . . . . . . 658--659
H. A. ShahAli and
Michael Reid Powers of Consecutive Integers: 11121 659--660
Li Zhou and
Michael Avidon An Inequality of Cosines and Sines:
11127 . . . . . . . . . . . . . . . . . 660--661
N. G. de Bruijn and
Rolf Richberg Sum of a Series: 11131 . . . . . . . . . 661--662
David E. Zitarelli Book Review: \booktitleWhen Computers
Were Human, by David Alan Grier . . . . 663--668
Bruce P. Palka Editor's Endnotes . . . . . . . . . . . 669--672
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Kevin O'Bryant and
Bruce Reznick and
Monika Serbinowska Almost Alternating Sums . . . . . . . . 673--688
Daniel J. Velleman Exponential vs. Factorial . . . . . . . 689--704
Jeff Suzuki Lagrange's Proof of the Fundamental
Theorem of Algebra . . . . . . . . . . . 705--714
Alois Kufner and
Lech Maligranda and
Lars-Erik Persson The Prehistory of the Hardy Inequality 715--732
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-Sixth William Lowell Putnam
Mathematical Competition . . . . . . . . 733--743
Héctor E. Lomelí and
César L. García Variations on a Theorem of Korovkin . . 744--750
Ian Abramson and
Larry Goldstein A Statistical Characterization of
Regular Simplices . . . . . . . . . . . 750--752
Lyle N. Long and
Howard Weiss How Terminal Is Terminal Velocity? . . . 752--755
Dinesh Singh The Spectrum in a Banach Algebra . . . . 756--758
Donald Knuth Problem 11243 . . . . . . . . . . . . . 759--759
Jolene Harris and
Bogdan Suceav\va Problem 11244 . . . . . . . . . . . . . 759--760
Cezar Lupu and
Tudorel Lupu Problem 11245 . . . . . . . . . . . . . 760--760
Lee Goldstein Problem 11246 . . . . . . . . . . . . . 760--760
Jürgen Eckhoff Problem 11247 . . . . . . . . . . . . . 760--760
Pál Péter Dályay Problem 11248 . . . . . . . . . . . . . 760--760
David Beckwith Problem 11249 . . . . . . . . . . . . . 760--760
Benne de Weger and
Microsoft Research Problems Group How Many Powers of 2 Must Survive? 11114 760--761
Michael Nyblom and
Giulio Francot and
Roberto Tauraso Counting Powers by Inclusion and
Exclusion: 11117 . . . . . . . . . . . . 762--762
Bob Berk and
Larry Shepp Gaussian Convex Hull: 11120 . . . . . . 762--763
Shahin Amrahov and
Andrew D. Loveless Now, What Year Is It? 11125 . . . . . . 763--763
Raymond Mortini and
Patrick J. Fitzsimmons Countably Linearly Independent: 11136 763--764
Grahame Bennett and
O. P. Lossers An Odd Inequality: 11139 . . . . . . . . 764--764
Walther Janous and
Rolf Richberg A Completely Monotonic Function: 11140 764--765
Richard Bagby and
O. P. Lossers Implicit Derivative Continuous: 11141 765--766
Joel Zinn and
Grahame Bennett A Sum Inequality: 11145 . . . . . . . . 766--766
Ramesh Gangolli Book Review: \booktitleDark Hero of the
Information Age: In Search of Norbert
Wiener, the Father of Cybernetics, by
Flo Conway; Jim Siegelman . . . . . . . 767--774
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Gabriel Katz Curves in Cages: An Algebro-Geometric
Zoo . . . . . . . . . . . . . . . . . . 777--791
Ion Barbu and
Sarah Glaz and
JoAnne Growney Ut Algebra Poesis (As Algebra, So
Poetry) . . . . . . . . . . . . . . . . 792--793
Aaron Melman and
Bill Gragg An Optimization Framework for Polynomial
Zerofinders . . . . . . . . . . . . . . 794--804
Glen Anderson and
Mavina Vamanamurthy and
Matti Vuorinen Monotonicity Rules in Calculus . . . . . 805--816
Ingram Olkin and
Larry Shepp Several Colorful Inequalities . . . . . 817--822
David F. Snyder Combinatorics of Barycentric Subdivision
and Characters of Simplicial
Two-Complexes . . . . . . . . . . . . . 822--826
Thomas Brady and
Colum Watt On Products of Euclidean Reflections . . 826--829
Vilmos Komornik Another Short Proof of Descartes's Rule
of Signs . . . . . . . . . . . . . . . . 829--830
Piotr Pragacz and
Abe Shenitzer and
John Stillwell and
Roman Duda The Life and Work of Alexander
Grothendieck . . . . . . . . . . . . . . 831--846
Sun Wen Cai Problem 11250 . . . . . . . . . . . . . 847--847
Marian Tetiva Problem 11251 . . . . . . . . . . . . . 847--847
Ovidiu Bagdasar Problem 11252 . . . . . . . . . . . . . 847--847
David Beckwith Problem 11253 . . . . . . . . . . . . . 847--847
Lenny Jones Problem 11254 . . . . . . . . . . . . . 847--848
Slavko Simic Problem 11255 . . . . . . . . . . . . . 848--848
Finbarr Holland Problem 11256 . . . . . . . . . . . . . 848--848
Gerd Herzog and
Roland Lemmert Problem 11242 . . . . . . . . . . . . . 848--848
Victor Pambuccian and
Robin Chapman Pythagorean Triangles Are Not Quite
Perfect: 11122 . . . . . . . . . . . . . 848--850
James S. Weber How Many Histograms Can a Data Set Have?
11126 . . . . . . . . . . . . . . . . . 850--851
Yongge Tian and
Robin Chapman Inequalities Involving Rank and
Kronecker Product: 11129 . . . . . . . . 851--851
Paul Bateman and
Michael R. Avidon Approximating the Reciprocal of Zeta:
11130 . . . . . . . . . . . . . . . . . 852--854
Pamela Gorkin and
Raymond Mortini and
the Microsoft Research Problems Group A Meromorphic Function: 11147 . . . . . 854--854
Charles R. Hampton Book Review: \booktitlePhilosophy of
Mathematics: An Introduction to the
World of Proofs Pictures, by James
Robert Brown; Philosophies of
Mathematics ~by Alexander George; Daniel
J. Velleman; Thinking about Mathematics:
The Philosophy of Mathematics ~by
Stewart Shapiro . . . . . . . . . . . . 855--860
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Emmanuel Kowalski Bernstein Polynomials and Brownian
Motion . . . . . . . . . . . . . . . . . 865--886
Rachel W. Hall and
Paul Klingsberg Asymmetric Rhythms and Tiling Canons . . 887--896
Pamela B. Pierce and
Daniel J. Velleman Some Generalizations of the Notion of
Bounded Variation . . . . . . . . . . . 897--904
Richard O. Hill and
Thomas H. Parker A Study of Core-Plus Students Attending
Michigan State University . . . . . . . 905--921
Andrew J. Simoson Sliding along a Chord through a Rotating
Earth . . . . . . . . . . . . . . . . . 922--928
A. G. Ramm Dynamical Systems Method and a
Homeomorphism Theorem . . . . . . . . . 928--933
Benjamin Baumslag A Simple Way of Proving the
Jordan--Hölder--Schreier Theorem . . . . 933--935
Andrew Browder Complex Numbers and the Ham Sandwich
Theorem . . . . . . . . . . . . . . . . 935--937
Filip Saidak A New Proof of Euclid's Theorem . . . . 937--938
Raimond Struble Problem 11257 . . . . . . . . . . . . . 939--939
Manuel Kauers Problem 11258 . . . . . . . . . . . . . 939--939
Nobuhisa Abe Problem 11259 . . . . . . . . . . . . . 939--939
Paolo Perfetti Problem 11260 . . . . . . . . . . . . . 939--939
Isaac Sofair Problem 11261 . . . . . . . . . . . . . 940--940
Ashay Burungale Problem 11262 . . . . . . . . . . . . . 940--940
Gregory Keselman Problem 11263 . . . . . . . . . . . . . 940--940
Christoph Soland Secondary Inradii: 11046 . . . . . . . . 940--941
Arturas Dubickas and
Chris Smyth and
Richard Stong Polynomials with Three Distinct Zeros
Summing to Zero: 11123 . . . . . . . . . 941--942
Ray Redheffer and
Richard Stong A Cousin of Gronwall's Inequality: 11135 942--943
Roberto Tauraso and
O. P. Lossers Perfect Squares From Punctured Squares:
11138 . . . . . . . . . . . . . . . . . 943--944
Mircea Ivan and
Microsoft Research Problems Group Patrial Fractions, Product Log: 11152 945--945
Emmanuel Kowalski and
Tanguy Rivoall A Positive Polynomial: 11155 . . . . . . 945--946
Anonymous Errata and End Notes for 2006 . . . . . 946--946
Della D. Fenster Book Review: \booktitleSaunders Mac
Lane: A Mathematical Autobiography, by
Saunders Mac Lane . . . . . . . . . . . 947--951
Steven Galovich Book Review: \booktitleAnts, Bikes, and
Clocks: Problem Solving for
Undergraduates, by William Briggs . . . 951--954
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Anonymous Volume Information . . . . . . . . . . . ??
Peter Maier and
Werner Nickel Attainable Patterns in Alien Tiles . . . 1--13
Tanya Leise and
Andrew Cohen Nonlinear Oscillators at Our Fingertips 14--28
Dave Auckly Solving the Quartic with a Pencil . . . 29--39
Donatella Merlini and
Renzo Sprugnoli and
Maria Cecilia Verri The Method of Coefficients . . . . . . . 40--57
William F. Ford and
James A. Pennline When Does Convergence in the Mean Imply
Uniform Convergence? . . . . . . . . . . 58--60
\vSime Ungar The Koch Curve: a Geometric Proof . . . 61--66
Dong-Soo Kim and
Young Ho Kim A Characterization of Ellipses . . . . . 66--70
Jonathan M. Borwein A Class of Dirichlet Series Integrals 70--76
Donald Knuth Problem 11264 . . . . . . . . . . . . . 77--77
Steve Butler and
Jia Mao Problem 11265 . . . . . . . . . . . . . 77--77
Marian Tetiva Problem 11266 . . . . . . . . . . . . . 77--77
Eugene A. Herman Problem 11267 . . . . . . . . . . . . . 77--77
M. L. Glasser Problem 11268 . . . . . . . . . . . . . 78--78
Hervé Moulin Problem 11269 . . . . . . . . . . . . . 78--78
Sergey Sadov Problem 11270 . . . . . . . . . . . . . 78--78
David Beckwith An Accidental Repetition of the All-Ones
Problem: 10851 . . . . . . . . . . . . . 78--79
Tom Apostol and
Microsoft Research Problems Group Summing the Initial Inverted Powers:
11128 . . . . . . . . . . . . . . . . . 79--80
M. L. Glasser and
Richard Stong An Elementary Integral: 11148 . . . . . 80--81
Mircea Ivan and
loan Rasa and
M. A. Prasad Limit with Nested Logs: 11149 . . . . . 81--81
Paul Bracken and
Michael Goldenberg and
Mark Kaplan A Nonlinear Recurrence: 11153 . . . . . 81--82
Hillel Gauchman and
Northwestern University Math Problem Solving Group Square Root Inequality: 11157 . . . . . 82--83
Greg Oman and
Michael W. Botsko Isomorphic Rings of Functions: 11166 . . 83--83
Mohammad Hossein Mehrabi and
O. P. Lossers A Gamma Function Inequality: 11169 . . . 83--84
Slavko Simic and
GCHQ Problem Solving Group Maximum Real Part of a Zero of a
Polynomial: 11184 . . . . . . . . . . . 84--84
Fernando Q. Gouvêa Book Review: \booktitleA First Course in
Modular Forms, by Fred Diamond; Jerry
Shurman . . . . . . . . . . . . . . . . 85--90
Daniel J. Velleman Editor's Endnotes . . . . . . . . . . . 91--91
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Richard K. Guy The Lighthouse Theorem, Morley &
Malfatti: a Budget of Paradoxes . . . . 97--141
Po-Ru Loh Stepping to Infinity Along Gaussian
Primes . . . . . . . . . . . . . . . . . 142--151
Bau-Sen Du A Simple Proof of Sharkovsky's Theorem
Revisited . . . . . . . . . . . . . . . 152--155
Gwen Spencer and
Francis Edward Su The LSB Theorem Implies the KKM Lemma 156--159
Sam B. Nadler, Jr. and
Donna M. Zitney Pointwise Products of Uniformly
Continuous Functions on Sets in the Real
Line . . . . . . . . . . . . . . . . . . 160--163
Iliya Bluskov Problem 11271 . . . . . . . . . . . . . 164--164
Vasile Mihai Problem 11272 . . . . . . . . . . . . . 164--164
Marian Tetiva Problem 11273 . . . . . . . . . . . . . 164--165
Donald Knuth Problem 11274 . . . . . . . . . . . . . 165--165
Michael S. Becker Problem 11275 . . . . . . . . . . . . . 165--165
Eugene Herman Problem 11276 . . . . . . . . . . . . . 165--165
Vicen\ctiu R\uadulescu and
Richard Stong Exponential Growth of a Solution: 11137 165--166
George Lamb and
J. A. Grzesik A Quadrature on a Sphere: 11159 . . . . 167--167
Paolo Perfetti and
Microsoft Research Problems Group Series with Sines: 11162 . . . . . . . . 167--168
Vicen\ctiu R\uadulescu and
Microsoft Research Problems Group Ginzburg--Landau Energy: 11167 . . . . . 168--170
Suat Namli and
O. P. Lossers A Functional Equation with Exponential
Solutions: 11180 . . . . . . . . . . . . 170--171
Grahame Bennett and
Eugene A. Herman Apply Hölder: 11202 . . . . . . . . . . . 171--171
Gerald B. Folland Book Review: \booktitleAnalysis I:
Convergence, Elementary Functions, by
Roger Godement; Analysis II:
Differential and Integral Calculus,
Fourier Series, Holomorphic Functions
~by Roger Godement . . . . . . . . . . . 172--176
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Amy Cohen-Corwin Yueh-Gin Gung and Dr. Charles Y. Hu
Award to Lee Lorch for Distinguished
Service to Mathematics . . . . . . . . . 181--182
Robyn Curtis and
Marcel Steiner Configuration Spaces of Planar Pentagons 183--201
Katherine Socha Circles in Circles: Creating a
Mathematical Model of Surface Water
Waves . . . . . . . . . . . . . . . . . 202--216
Anders Claesson and
T. Kyle Petersen Conway's Napkin Problem . . . . . . . . 217--231
Dante Manna and
Victor H. Moll A Simple Example of a New Class of
Landen Transformation . . . . . . . . . 232--241
Michael W. Botsko Exactly Which Bounded Darboux Functions
Are Derivatives? . . . . . . . . . . . . 242--246
Mark Levi Riemann Mapping Theorem by Steepest
Descent . . . . . . . . . . . . . . . . 246--251
David H. Armitage Entire Functions That Tend to Zero on
Every Line . . . . . . . . . . . . . . . 251--256
Mark A. Pinsky Stirling's Formula via the Poisson
Distribution . . . . . . . . . . . . . . 256--258
Prithwijit De Problem 11277 . . . . . . . . . . . . . 259--259
Slavko Simic Problem 11278 . . . . . . . . . . . . . 259--259
Vitaly Stakhovsky Problem 11279 . . . . . . . . . . . . . 259--259
Harris Kwong Problem 11280 . . . . . . . . . . . . . 259--259
Max Alekseyev and
Emeric Deutsch Problem 11281 . . . . . . . . . . . . . 259--259
Dragomir \vZ. \Dbarkovi\'c and
Kaiming Zhao Problem 11282 . . . . . . . . . . . . . 260--260
John Abbot and
Umberto Zannier Problem 11283 . . . . . . . . . . . . . 260--260
Stephen B. Gray and
Thomas McMillan and
Xiaoshen Wang Stepping to Regularity: 10923 . . . . . 260--261
Kent D. Boklan and
Michael R. Avidon Heronian Triangles: 11134 . . . . . . . 261--262
Ernst Schulte-Geers and
Karl David An Identity Involving Rooted Forest:
11144 . . . . . . . . . . . . . . . . . 262--264
Yongge Tian and
Eugene A. Herman Matrix Systems with the Same Sets: 11146 264--264
Emeric Deutsch and
O. P. Lossers Peaks in Dyck Paths: 11150 . . . . . . . 264--265
Donald E. Knuth and
O. P. Lossers Partitions of a Circular Set: 11151 . . 265--266
Kent Holing and
Michael R. Avidon Indivisibility of the Sum of Squares:
11154 . . . . . . . . . . . . . . . . . 266--266
John Stillwell Book Review: \booktitleGod Created the
Integers, by Stephen Hawking . . . . . . 267--271
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Alberto A. Martínez Euler's ``Mistake''? The Radical Product
Rule in Historical Perspective . . . . . 273--285
Christopher Francese and
David Richeson The Flaw in Euler's Proof of His
Polyhedral Formula . . . . . . . . . . . 286--296
Gopala Krishna Srinivasan The Gamma Function: An Eclectic Tour . . 297--315
Bennett Chow and
David Glickenstein Semidiscrete Geometric Flows of Polygons 316--328
Colin Adams and
Frank Morgan and
John M. Sullivan When Soap Bubbles Collide . . . . . . . 329--337
Arthur T. Benjamin and
Gregory P. Dresden A Combinatorial Proof of Vandermonde's
Determinant . . . . . . . . . . . . . . 338--341
Michael A. Allen Evaluation of Some Improper Integrals
Involving Hyperbolic Functions . . . . . 341--343
Robin Pemantle and
Carsten Schneider When Is 0.999\ldots Equal to 1? . . . . 344--350
Brendan Foreman Ghys's Theorem and Semi-Osculating
Conics of Planar Curves . . . . . . . . 351--356
Gilbert Helmberg An Absolutely Continuous Function in L1
(R) W1,1 (R) . . . . . . . . . . . . . . 356--357
Greg Oman Problem 11284 . . . . . . . . . . . . . 358--358
Yakub Aliyev Problem 11285 . . . . . . . . . . . . . 358--358
Marc LeBrun and
David Applegate and
N. J. A. Sloane Problem 11286 . . . . . . . . . . . . . 358--358
Stephen J. Herschkorn Problem 11287 . . . . . . . . . . . . . 359--359
Christopher Hillar and
Troels Windfeldt Problem 11288 . . . . . . . . . . . . . 359--359
Oleh Faynshteyn Problem 11289 . . . . . . . . . . . . . 359--359
Cezar Lupu and
Tudorel Lupu Problem 11290 . . . . . . . . . . . . . 359--359
Jonathan Sondow and
Richard Stong Choice Bounds: 11132 . . . . . . . . . . 359--360
Paul Bracken and
Heinz-Jürgen Seiffert An Integral Inequality: 11133 . . . . . 360--361
Donald Knuth and
Roberto Tauraso A Combinatorial Maximum: 11142 . . . . . 361--362
Richard Stanley and
GCHQ Problem Solving Group Inverting a Matrix of Striling Numbers:
11156 . . . . . . . . . . . . . . . . . 362--362
Emeric Deutsch and
Lafayette College Problem Group Compositions without Common Factors:
11161 . . . . . . . . . . . . . . . . . 363--363
Michel Bataille and
Richard Stong Counting Lattice Quadrilaterals Tangent
to an Ellipse: 11163 . . . . . . . . . . 363--364
José Luis Díaz-Barrero and
Ulrich Abel and
Mircea Ivan A Recurrent Identify: 11164 . . . . . . 364--365
John P. D'Angelo Book Review: \booktitleGeometric
Function Theory: Explorations in Complex
Analysis, by Steven G. Krantz . . . . . 366--370
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Yuval Peres and
Oded Schramm and
Scott Sheffield and
David B. Wilson Random-Turn Hex and Other Selection
Games . . . . . . . . . . . . . . . . . 373--387
Tom M. Apostol and
Mamikon A. Mnatsakanian Unwrapping Curves from Cylinders and
Cones . . . . . . . . . . . . . . . . . 388--416
Graham Everest and
Shaun Stevens and
Duncan Tamsett and
Tom Ward Primes Generated by Recurrence Sequences 417--431
J. W. Neuberger The Continuous Newton's Method, Inverse
Functions, and Nash--Moser . . . . . . . 432--437
Anthony Mendes A Note on Alternating Permutations . . . 437--440
Michael Kerckhove and
Gary Lawlor The Circle and the Cycloid: a Surprising
Link . . . . . . . . . . . . . . . . . . 441--443
Jack Ohm A Matrix Approach to Zero-Divisors in
R[x] . . . . . . . . . . . . . . . . . . 444--450
Richard Jerrard and
John Wetzel Problem 11291 . . . . . . . . . . . . . 451--451
David Callan Problem 11292 . . . . . . . . . . . . . 451--451
Sergey Sadov Problem 11293 . . . . . . . . . . . . . 451--451
John Zucker and
Ross McPhedran Problem 11294 . . . . . . . . . . . . . 452--452
Stefano Siboni Problem 11295 . . . . . . . . . . . . . 452--452
Said Amghibech Problem 11296 . . . . . . . . . . . . . 452--452
Marian Tetiva Problem 11297 . . . . . . . . . . . . . 452--452
Bogdan Nica and
S. Amghibech Similarities of Euclidean Space: 11124 452--453
Alexander Dubinov and
Irina Dubinova Closed Form Closure: 11143 . . . . . . . 453--453
David Beckwith and
Harris Kwong Prime Powers Dividing a Factorial: 11158 453--454
Marc Chamberland and
C. R. Pranesachar Fermat to the Rescue: 11160 . . . . . . 454--454
Yogesh More and
Robin Chapman The Sum of Catalan Numbers, Modulo 3:
11165 . . . . . . . . . . . . . . . . . 454--455
Kent Holing and
Microsoft Research Problems Group Properties of Pythagorean Triples: 11168 455--456
Emeric Deutsch and
S. C. Locke Dissecting a Polygon: 11170 . . . . . . 456--457
Heinz-Jürgen Seiffert Familiar Identities in Disguise: 11172 457--458
David M. Bressoud Book Review: \booktitleMaking
Transcendence Transparent, by B. Burger;
Robert Tubbs . . . . . . . . . . . . . . 459--461
Mark Schwartz Book Review: \booktitleConics, by Keith
Kendig . . . . . . . . . . . . . . . . . 461--464
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Brian S. Thomson Rethinking the Elementary Real Analysis
Course . . . . . . . . . . . . . . . . . 469--490
Andrew J. Hetzel and
Jay S. Liew and
Kent E. Morrison The Probability That a Matrix of
Integers Is Diagonalizable . . . . . . . 491--499
Brody Dylan Johnson The Nonholonomy of the Rolling Sphere 500--508
Dierk Schleicher Hausdorff Dimension, Its Properties, and
Its Surprises . . . . . . . . . . . . . 509--528
Ling-Ling Shi and
Hao Pan A $q$-Analogue of Wolstenholme's
Harmonic Series Congruence . . . . . . . 529--531
Jürgen Bliedtner and
Peter A. Loeb A Local Maximal Function Simplifying
Measure Differentiation . . . . . . . . 532--536
Boris Adamczewski and
Yann Bugeaud A Short Proof of the Transcendence of
Thue--Morse Continued Fractions . . . . 536--540
Joseph Bak and
Pisheng Ding and
Donald Newman Extremal Points, Critical Points, and
Saddle Points of Analytic Functions . . 540--546
Jakob Jonsson Problem 11298 . . . . . . . . . . . . . 547--547
Pablo Fern\`andez Refolio Problem 11299 . . . . . . . . . . . . . 547--547
Ulrich Abel Problem 11300 . . . . . . . . . . . . . 547--547
Finbarr Holland Problem 11301 . . . . . . . . . . . . . 547--547
Horst Alzer Problem 11302 . . . . . . . . . . . . . 547--547
M. Farrokhi Problem 11303 . . . . . . . . . . . . . 548--548
Teodora-Liliana R\uadulescu Problem 11304 . . . . . . . . . . . . . 548--548
M. N. Deshpande and
J. P. Shiwalkar and
GCHQ Problem Solving Group Two Heads Are Better than One: 11173 . . 548--549
Jon Bentley and
Colin Mallows and
Richard Stong Learning from Experience: 11178 . . . . 549--550
David Beckwith and
Li Zhou A Determinant by Möbius Inversion: 11179 550--550
Shahin Amrahov and
Nicholas C. Singer Perfect Powers in an Arithmetic
Progression: 11182 . . . . . . . . . . . 550--551
David Beckwith and
Vadim Ponomarenko and
Rob Pratt Building Two Piles of Equal Height:
11183 . . . . . . . . . . . . . . . . . 551--552
Rainer Brück and
Robin Chapman When Does It Converge: 11185 . . . . . . 552--554
Li Zhou and
Northwestern University Math Problem Solving Group and
Christopher Carl Heckman and
Jerry Minkus Tiling $4$-Rowed Rectangles with
Dominoes: 11187 . . . . . . . . . . . . 554--556
Susan Jane Colley Book Review: \booktitleIntroduction to
Plane Algebraic Curves, by Ernst Kunz;
Richard G. Belshoff . . . . . . . . . . 557--561
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Enrique A. González- Velasco James Gregory's Calculus in the
``Geometriæ Pars Universalis'' . . . . . 565--576
Roman Dwilewicz and
Ján Miná\vc and
Andrew Schultz and
John Swallow Hilbert 90 for Biquadratic Extensions 577--587
Arno Berger and
Theodore P. Hill Newton's Method Obeys Benford's Law . . 588--601
Jin Akiyama Tile-Makers and Semi-Tile-Makers . . . . 602--609
Byron L. Walden and
Lesley A. Ward A Harmonic Measure Interpretation of the
Arithmetic-Geometric Mean . . . . . . . 610--622
Carlos A. Escudero and
Agustí Reventós An Interesting Property of the Evolute 623--628
Jack Cook and
Jonathan Lovett and
Frank Morgan Rotation in a Normed Plane . . . . . . . 628--632
Arjeh M. Cohen and
D. E. Taylor On a Certain Lie Algebra Defined by a
Finite Group . . . . . . . . . . . . . . 633--639
Vahan Mkrtchyan Problem 11305 . . . . . . . . . . . . . 640--640
Alexandru Rosoiu Problem 11306 . . . . . . . . . . . . . 640--640
David Callan Problem 11307 . . . . . . . . . . . . . 640--640
Ovidiu Furdui Problem 11308 . . . . . . . . . . . . . 640--640
Roman Witu\la and
Damian S\lota Problem 11309 . . . . . . . . . . . . . 640--640
Erwin Just Problem 11310 . . . . . . . . . . . . . 641--641
Stephen J. Herschkorn Problem 11311 . . . . . . . . . . . . . 641--641
William Calbeck and
Richard Stong Another Diophantine Equation: 11175 . . 641--642
M. N. Deshpande and
GCHQ Problem Solving Group An Urn Problem with Labeled and
Unlabeled Balls: 11181 . . . . . . . . . 642--642
Angelo J. Christino, Jr. and
William C. Waterhouse and
the NSA Problems Group A Group of Invertible Matrices: 11186 642--643
David Bailey and
M. L. Glasser and
Richard Stong A Hypergeometric Identity: 11188 . . . . 643--645
Lajos Csete and
O. P. Lossers A Quick Inequality: 11189 . . . . . . . 645--645
José Luis Díaz-Barrero and
Julien Grivaux A Polynomial and Its Zeros: 11190 . . . 645--647
Marian Tetiva A Cyclic AM-GM Inequality: 11193 . . . . 647--647
Marian Tetiva and
Pál Péter Dályay Ratio Circum-to-In-Radius: 11195 . . . . 648--649
R. A. Strubel and
Donald R. Bridges A Zeta Function Quickie: 11219 . . . . . 649--649
Aliyev Yakub and
David B. Leep Symmetric Inequality: 11199 . . . . . . 649--649
Stephen A. Fulling Book Review: \booktitleLinearity,
Symmetry, and Prediction in the Hydrogen
Atom, by Stephanie Frank Singer . . . . 650--653
James Fey and
Eric Hart and
Christian Hirsch and
Harold Schoen and
Ann Watkins and
Daniel J. Velleman Editor's Endnotes . . . . . . . . . . . 654--661
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
David Benko A New Approach to Hilbert's Third
Problem . . . . . . . . . . . . . . . . 665--676
John H. Jaroma and
Kamaliya N. Reddy Classical and Alternative Approaches to
the Mersenne and Fermat Numbers . . . . 677--687
Gábor J. Székely and
Maria L. Rizzo The Uncertainty Principle of Game Theory 688--702
Harm Derksen and
Christian Eggermont and
Arno van den Essen Multimagic Squares . . . . . . . . . . . 703--713
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-Seventh William Lowell Putnam
Mathematical Competition . . . . . . . . 714--724
Peter D. Lax The Cauchy Integral Theorem . . . . . . 725--727
Folkmar Bornemann and
Thomas Schmelzer Taming a Hydra of Singularities . . . . 727--732
M. Ram Murty and
Nithum Thain Pick's Theorem via Minkowski's Theorem 732--736
F. Albiac and
N. J. Kalton A Characterization of Real $ C(K)
$-Spaces . . . . . . . . . . . . . . . . 737--743
David Callan Problem 11312 . . . . . . . . . . . . . 744--744
Cezar Lupu and
Tudorel Lupu Problem 11313 . . . . . . . . . . . . . 744--744
Yakub Aliyev Problem 11314 . . . . . . . . . . . . . 744--744
M. Farrokhi Problem 11315 . . . . . . . . . . . . . 744--744
Ovidiu Furdui Problem 11316 . . . . . . . . . . . . . 745--745
Michel Bataille Problem 11317 . . . . . . . . . . . . . 745--745
Roman Witu\la and
Damian S\lota Problem 11318 . . . . . . . . . . . . . 745--745
R. V. Heath and
Christian Boyer Better Late than Never: E 496 . . . . . 745--746
Folkmar Bornemann and
Robert B. Israel A Disguised Radius of Convergence: 11194 746--747
Oleg Faynshteyn and
Arkady Alt A Crux Inequality: 11197 . . . . . . . . 747--748
Joel Zinn and
O. P. Lossers Kronecker-Like Convergence: 11200 . . . 748--749
Michael S. Becker and
Zuofeng Shang Cosine Infinite Product: 11210 . . . . . 749--749
Mihály Bencze and
Heinz-Jürgen Seiffert More A-G Inequalities: 11211 . . . . . . 749--750
José Luis Díaz-Barrero and
Eugene Herman Limit of an Integral: 11225 . . . . . . 750--750
Ovidiu Furdui and
Michael R. Avidon A Gamma Limit: 11229 . . . . . . . . . . 751--751
Warren P. Johnson Book Review: \booktitleMathematics and
Social Utopias in France: Olinde
Rodrigues and His times, by Simon
Altmann; Eduardo L. Ortiz . . . . . . . 752--758
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Thomas Callaghan and
Peter J. Mucha and
Mason A. Porter Random Walker Ranking for NCAA Division
I-A Football . . . . . . . . . . . . . . 761--777
John Starrett Solving Differential Equations by
Symmetry Groups . . . . . . . . . . . . 778--792
Tomasz Bartnicki and
Jaroslaw Grytczuk and
H. A. Kierstead and
Xuding Zhu The Map-Coloring Game . . . . . . . . . 793--803
Hugh L. Montgomery and
Ulrike M. A. Vorhauer Biased Trigonometric Polynomials . . . . 804--809
Omer Adelman $ \sum \frac {1}{n} = \infty $: a
Micro-Lesson on Probability and Symmetry 809--810
Benjamin A. Lotto Stacked Groups . . . . . . . . . . . . . 811--812
Brett A. Harrison On the Reducibility of Cyclotomic
Polynomials over Finite Fields . . . . . 813--818
Marston Morse Topology and Equilibria . . . . . . . . 819--834
David Beckwith Problem 11319 . . . . . . . . . . . . . 835--835
Donald Knuth Problem 11320 . . . . . . . . . . . . . 835--835
Christopher Hillar Problem 11321 . . . . . . . . . . . . . 835--835
Jonathan Sondow Problem 11322 . . . . . . . . . . . . . 835--835
Jody M. Lockhart and
William P. Wardlaw Problem 11323 . . . . . . . . . . . . . 835--835
Martin Kochanski Problem 11324 . . . . . . . . . . . . . 836--836
Finbarr Holland and
Jim Leahy Problem 11325 . . . . . . . . . . . . . 836--836
José Luis Díaz-Barrero and
Pantelimon George Popescu Problem 11326 . . . . . . . . . . . . . 836--836
Pál Péter Dályay and
National Security Agency Problems Group Periodic Composition: 11174 . . . . . . 836--837
Oleg Faynshteyn and
Yan-loi Wong Another Triangle Inequality: 11176 . . . 837--838
Dorin M\varghidanu and
Henry Ricardo $ {\rm GM} \leq {\rm AMF} $: 11177 . . . 838--838
Barthel Wayne Huff and
Gregory Keselman Another Urn and Balls Problem: 11191 . . 838--839
Brett Stevens and
Richard Stong A Sudoku Solution from Orthogonal Latin
Squares: 11192 . . . . . . . . . . . . . 839--840
Fuxiang Yu An Old Fermatian Problem: 11203 . . . . 840--840
Christopher J. Hillar and
John H. Lindsey II and
Robin Chapman The Trace of the Sum of All Products of
Two Matrices: 11204 . . . . . . . . . . 840--841
Li Zhou and
Chris Mackeprang and
Kellen Myers Coloring Graphs on Sponges: 11208 . . . 842--842
Edward Nelson Book Review: \booktitle18 Unconventional
Essays on the Nature of Mathematics, by
Reuben Hersh . . . . . . . . . . . . . . 843--848
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Charles R. Hadlock Practicing Mathematics in the Public
Arena: Challenges and Outcomes in Some
Prominent Case Studies . . . . . . . . . 849--870
Markku Halmetoja and
Pentti Haukkanen and
Teuvo Laurinolli and
Jorma K. Merikoski and
Timo Tossavainen and
Ari Virtanen On Direct and Inverse Proportionality 871--881
Thomas C. Hales The Jordan Curve Theorem, Formally and
Informally . . . . . . . . . . . . . . . 882--894
Mark Levi and
Serge Tabachnikov The Poncelet Grid and Billiards in
Ellipses . . . . . . . . . . . . . . . . 895--908
Alain Connes and
Don Zagier A Property of Parallelograms Inscribed
in Ellipses . . . . . . . . . . . . . . 909--914
Johan Wästlund An Elementary Proof of the Wallis
Product Formula for $ \pi $ . . . . . . 914--917
Christopher J. Hillar and
Darren L. Rhea Automorphisms of Finite Abelian Groups 917--923
António Guedes de Oliveira On the Adjugate of a Matrix . . . . . . 923--924
Rick Mabry and
Debbie Shepherd Problem 11327 . . . . . . . . . . . . . 925--925
Dmitris Vartziotis Problem 11328 . . . . . . . . . . . . . 925--925
T. Amdeberhan and
Victor H. Moll Problem 11329 . . . . . . . . . . . . . 925--925
Marian Tetiva Problem 11330 . . . . . . . . . . . . . 925--925
Richard Bagby Problem 11331 . . . . . . . . . . . . . 926--926
Roberto Tauraso Problem 11332 . . . . . . . . . . . . . 926--926
Pablo Fernández Refolio Problem 11333 . . . . . . . . . . . . . 926--926
Chu Cheng and
Marius Stefan A Quadrilateral and Its Circles: 11171 926--927
Wu Wei Chao and
Pál Péter Dályay A Triangle Inequality: 11205 . . . . . . 928--928
Mircea Ivan and
Alexandru Lupa\cs and
Richard A. Stong A Limit Involving Euler's Constant:
11206 . . . . . . . . . . . . . . . . . 928--929
Michael W. Botsko and
Robert B. Israel Disguised Cauchy Sequence: 11207 . . . . 929--930
Alexander Dubinov and
Irina Dubinova and
Knut Dale Can ``Closed Form'' Involve Lambert?
11209 . . . . . . . . . . . . . . . . . 930--931
Michel Bataille and
Richard Stong Finding the Greatest Lower Bound: 11217 931--931
Anonymous Errata: 11307 . . . . . . . . . . . . . 932--932
Kent Holing Unsolved No Longer: 11154 . . . . . . . 932--932
Bogdan Nica Reverse Engineering: 11124 . . . . . . . 932--932
Michael Henle Book Review: \booktitleDivine
Proportions: Rational Trigonometry to
Universal Geometry, by N. J. Wildberger 933--937
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Anonymous Volume Information . . . . . . . . . . . ??
Frederick V. Henle and
James M. Henle Squaring the Plane . . . . . . . . . . . 3--12
Michelle Previte and
Sean Yang A Novel Way to Generate Fractals . . . . 13--32
Péter Komjáth and
Vilmos Totik Ultrafilters . . . . . . . . . . . . . . 33--44
Ray Cavalcante and
Todor D. Todorov A Lost Theorem: Definite Integrals in an
Asymptotic Setting . . . . . . . . . . . 45--56
Greg Martin A Simple Polynomial for a Simple
Transposition . . . . . . . . . . . . . 57--60
Banyat Sroysang and
John E. Wetzel and
Wacharin Wichiramala Covers for Angleworms . . . . . . . . . 61--65
Stefanie Ucsnay A Note on Tarski's Note . . . . . . . . 66--68
Simon Marshall Another Simple Proof of the High Girth,
High Chromatic Number Theorem . . . . . 68--70
Jonathan Bober and
Jeffrey Lagarias Problem 11334 . . . . . . . . . . . . . 71--71
Juan López González Problem 11335 . . . . . . . . . . . . . 71--71
Donald Knuth Problem 11336 . . . . . . . . . . . . . 71--71
Marian Tetiva Problem 11337 . . . . . . . . . . . . . 71--71
Ovidiu Furdui Problem 11338 . . . . . . . . . . . . . 71--71
José Luis Díaz-Barrero Problem 11339 . . . . . . . . . . . . . 72--72
Óscar Ciaurri and
Luz Roncal Problem 11340 . . . . . . . . . . . . . 72--72
Mohammad Hossein Mehrabi and
Pál Péter Dályay A Condition on the Commutator: 11196 . . 72--72
Robert Russell and
Christoph Soland and
William Dickinson and
William Dickenson Can One Recover a (Spherical) Triangle
from Its Medial Triangle? 11201 . . . . 73--74
Paolo Perfetti and
Richard Bagby Differentiable and Discontinuous
Densely: 11221 . . . . . . . . . . . . . 74--75
Christopher Hillar and
Lionel Levine and
S. C. Locke Snapshots for Velocities: 11223 . . . . 75--76
Franck Beaucoup and
Tamás Erdélyi and
Microsoft Research Problems Group A Unique Solution: 11226 . . . . . . . . 76--76
Michael W. Botsko and
Albert Stadler A Function Inequality: 11232 . . . . . . 77--77
Marian Tetiva and
Minh Can A Triangle Inequality: 11228 . . . . . . 77--77
Robert Downes and
Jean-Pierre Grivaux A Derivative Formula: 11233 . . . . . . 78--78
Jeffrey Nunemacher Book Review: \booktitleFearless
Symmetry: Exposing the Hidden Patterns
of Numbers, by Avner Ash; Robert Gross 79--82
Ron Solomon Book Review: \booktitleSymmetry and the
Monster, by Mark Ronan . . . . . . . . . 82--85
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Christopher S. Hardin and
Alan D. Taylor A Peculiar Connection between the Axiom
of Choice and Predicting the Future . . 91--96
Michel Balinski Fair Majority Voting (or How to
Eliminate Gerrymandering) . . . . . . . 97--113
Hugh Nelson Howards Brunnian Spheres . . . . . . . . . . . . 114--124
Jonathan M. Borwein Hilbert's Inequality and Witten's
Zeta-Function . . . . . . . . . . . . . 125--137
Abraham A. Ungar From Möbius to Gyrogroups . . . . . . . . 138--144
Aaron Melman Bounds on the Zeros of the Derivative of
a Polynomial with All Real Zeros . . . . 145--147
Uri Elias Qualitative Analysis of a Differential
Equation of Abel . . . . . . . . . . . . 147--149
W. Holszty\'nski and
J. Mycielski and
G. C. O'Brien and
S. \'Swierczkowski Closed Curves on Spheres . . . . . . . . 149--153
E. F. Cornelius, Jr. and
Phill Schultz Sequences Generated by Polynomials . . . 154--158
Krzysztof Ciesielski and
Zdzis\law Pogoda On Ordering the Natural Numbers, or, The
Sharkovski Theorem . . . . . . . . . . . 159--165
Cezar Lupu Problem 11341 . . . . . . . . . . . . . 166--166
Luis H. Gallardo Problem 11342 . . . . . . . . . . . . . 166--166
David Beckwith Problem 11343 . . . . . . . . . . . . . 166--166
Albert Stadler Problem 11344 . . . . . . . . . . . . . 166--166
Roger Cuculi\`ere Problem 11345 . . . . . . . . . . . . . 166--166
Christopher Hillar Problem 11346 . . . . . . . . . . . . . 166--167
Mihály Bencze Problem 11347 . . . . . . . . . . . . . 167--167
Solomon W. Golomb and
Kyle Calderhead Orthogonal Sudoku Squares: 11214 . . . . 167--168
Shmuel Rosset and
José Heber Nieto Maximum Velocity on a Car Trip: 11215 168--169
Jim Brennan and
Richard Ehrenborg and
Eugene A. Herman Goes Back to Boole: 11234 . . . . . . . 169--170
Jim Owings and
Marian Tetiva and
Matthew Huddleston Coloring the Plane: 11236 . . . . . . . 170--172
Pál Péter Dályay and
A. K. Shafie Ex-To-In-Radius Ratio: 11240 . . . . . . 172--172
Jolene Harris and
Bogdan Suceav\va and
Knut Dale Iterational Rate of Covergence: 11244 173--173
Marion Cohen Book Review: \booktitleLetters to a
Young Mathematician, by Ian Stewart . . 174--177
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Amy Cohen-Corwin Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2008 to Lida K. Barrett for
Distinguished Service to Mathematics . . 183--184
Fan Chung and
Ron Graham Primitive Juggling Sequences . . . . . . 185--194
Jin Akiyama and
Hiroshi Fukuda and
Chie Nara and
Toshinori Sakai and
Jorge Urrutia Universal Measuring Boxes with
Triangular Bases . . . . . . . . . . . . 195--201
Diego M. Benardete and
V. W. Noonburg and
B. Pollina Qualitative Tools for Studying Periodic
Solutions and Bifurcations as Applied to
the Periodically Harvested Logistic
Equation . . . . . . . . . . . . . . . . 202--219
Lee W. Jacobi and
Daniel J. Madden On $ a^4 + b^4 + c^4 + d^4 = (a + b + c
+ d)^4 $ . . . . . . . . . . . . . . . . 220--236
Takashi Agoh and
Karl Dilcher Reciprocity Relations for Bernoulli
Numbers . . . . . . . . . . . . . . . . 237--244
Krassimir Penev The Fubini Principle . . . . . . . . . . 245--248
Franciszek Prus-Wi\'sniowski A Refinement of Raabe's Test . . . . . . 249--252
Ay\cse Alaca and
\cSaban Alaca and
Kenneth S. Williams Arithmetic Progressions and Binary
Quadratic Forms . . . . . . . . . . . . 252--254
Peter W. Saltzman and
Pingzhi Yuan On Sums of Consecutive Integral Roots 254--261
Richard P. Stanley Problem 11348 . . . . . . . . . . . . . 262--262
Cezar Lupu Problem 11349 . . . . . . . . . . . . . 262--262
Bhavana Deshpande and
M. N. Deshpande Problem 11350 . . . . . . . . . . . . . 262--262
Marian Tetiva Problem 11351 . . . . . . . . . . . . . 262--262
Daniel Reem Problem 11352 . . . . . . . . . . . . . 263--263
Ernst Schulte-Geers Problem 11353 . . . . . . . . . . . . . 263--263
Matthias Beck and
Alexander Berkovich Problem 11354 . . . . . . . . . . . . . 263--263
Hans V. Gerber and
Daniel Neuenschwander Unsolved in 1990: 6576 . . . . . . . . . 263--264
Gerd Herzog and
Roland Lemmert A Determinant Indentity: 11242 . . . . . 264--265
Lee Goldstein A Bessel Function Identity: 11246 . . . 265--266
Jürgen Eckhoff and
Li Zhou A Strip Problem: 11247 . . . . . . . . . 266--266
Sun Wen Cai and
Vitaly Stakhovsky Double Sum Inequality: 11250 . . . . . . 266--267
Marian Tetiva and
Vitaly Stakhovsky An Inequality Proved Without Computer
Assistance: 11251 . . . . . . . . . . . 267--268
Ovidiu Bagdasar and
Marian Tetiva A Productive Inequality: 11252 . . . . . 268--269
Raimond Struble and
Jean-Pierre Grivaux A Myth About Infinite Products: 11257 269--269
Martin Davis Book Review: \booktitleInexhaustibility:
A Non-Exhaustive Treatment, by Torkel
Franzén; Gödel's Theorem: An Incomplete
Guide to Its Use and Misuse ~by Torkel
Franzén . . . . . . . . . . . . . . . . . 270--275
Anonymous Editor's Endnotes . . . . . . . . . . . 276--276
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Andrew Granville Prime Number Patterns . . . . . . . . . 279--296
Robert A. Agnew Optimal Congressional Apportionment . . 297--303
Steven G. Krantz The Carathéodory and Kobayashi Metrics
and Applications in Complex Analysis . . 304--329
Dan Kalman An Elementary Proof of Marden's Theorem 330--338
Mihály Bessenyei The Hermite--Hadamard Inequality on
Simplices . . . . . . . . . . . . . . . 339--345
John P. Robertson and
Keith R. Matthews A Continued Fractions Approach to a
Result of Feit . . . . . . . . . . . . . 346--349
Gerhard Larcher and
Friedrich Pillichshammer The Sum of Distances between Vertices of
a Convex Polygon with Unit Perimeter . . 350--355
Cayanne McFarlane and
Wm. Douglas Withers Dynamical Systems and Irrational Angle
Construction by Paper-Folding . . . . . 355--358
Marc Renault Lost (and Found) in Translation: André's
Actual Method and Its Application to the
Generalized Ballot Problem . . . . . . . 358--363
Amitabha Tripathi On Sums of Positive Integers That Are
Not of the Form $ a x + b y $ . . . . . 363--364
Jeffrey C. Lagarias Problem 11355 . . . . . . . . . . . . . 365--365
Michael Poghosyan Problem 11356 . . . . . . . . . . . . . 365--365
Mehmet \cSahin Problem 11357 . . . . . . . . . . . . . 365--365
Marian Tetiva Problem 11358 . . . . . . . . . . . . . 365--365
J. Monterde Problem 11359 . . . . . . . . . . . . . 365--365
Cezar Lupu Problem 11360 . . . . . . . . . . . . . 365--366
David Beckwith and
Harris Kwong and
Rob Pratt and
Nicholas Singer A Vanishing Alternating Sum: 11212/11220 366--366
Finbarr Holland Problem 11361 . . . . . . . . . . . . . 366--366
Stanley Rabinowitz and
NSA Problems Group Sometimes an Integer: 11213 . . . . . . 366--367
Gary Gordon and
Bruce S. Burdick The Number between $1$ and $n$ That Is
Least Prime: 11218 . . . . . . . . . . . 367--368
Pál Péter Dályay and
Jaime Vinuesa A Romanian Olympiad Problem Generalized:
11248 . . . . . . . . . . . . . . . . . 368--369
Slavko Simic and
O. P. Lossers A Symmetric Inequality: 11255 . . . . . 369--370
Finbarr Holland and
Michel Bataille Perimeter by Integral: 11256 . . . . . . 370--371
Gregory Keselman and
E. Leonard A Choice Sum: 11263 . . . . . . . . . . 371--372
Leslie Hogben and
Wolfgang Kliemann Book Review: \booktitleApplied Linear
Algebra, by Peter J. Olver; Chehrzad
Shakiban . . . . . . . . . . . . . . . . 373--378
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
R. A. Bailey and
Peter J. Cameron and
Robert Connelly Sudoku, Gerechte Designs, Resolutions,
Affine Space, Spreads, Reguli, and
Hamming Codes . . . . . . . . . . . . . 383--404
J. Arroyo and
O. J. Garay and
J. J. Mencía When Is a Periodic Function the
Curvature of a Closed Plane Curve? . . . 405--414
Hieu D. Nguyen Rearing Its Ugly Head: The Cosmological
Constant and Newton's Greatest Blunder 415--430
Jasbir S. Chahal and
Brian Osserman The Riemann Hypothesis for Elliptic
Curves . . . . . . . . . . . . . . . . . 431--442
Igor Pak Inflating the Cube Without Stretching 443--445
Robert Kantrowitz and
Michael M. Neumann Yet Another Proof of Minkowski's
Inequality . . . . . . . . . . . . . . . 445--447
Kathy Q. Ji and
Herbert S. Wilf Extreme Palindromes . . . . . . . . . . 447--451
F. Mendivil and
T. D. Taylor Thin Sets with Fat Shadows: Projections
of Cantor Sets . . . . . . . . . . . . . 451--456
Larry Eifler and
Noah H. Rhee The $n$-Dimensional Pythagorean Theorem
via the Divergence Theorem . . . . . . . 456--457
Grzegorz Rz\kadkowski Derivatives and Eulerian Numbers . . . . 458--460
David Callan Problem 11362 . . . . . . . . . . . . . 461--461
Oleh Faynshteyn Problem 11363 . . . . . . . . . . . . . 461--461
Pál Péter Dályay Problem 11364 . . . . . . . . . . . . . 461--462
Aviezri S. Fraenkel Problem 11365 . . . . . . . . . . . . . 462--462
Nicolae Anghel Problem 11366 . . . . . . . . . . . . . 462--462
Andrew Cusumano Problem 11367 . . . . . . . . . . . . . 462--462
Wei-Dong Jiang Problem 11368 . . . . . . . . . . . . . 462--462
P. R. Parthasarathy Generating Functions and Hypergeometric
Series and Continued Fractions! 11198 462--464
Ted Chinburg and
Shahriar Shahriari and
Reid Huntsinger Groups, Rings, Fields, and Power Series:
11216 . . . . . . . . . . . . . . . . . 464--465
Jonathan Sondow and
GCHQ Problem Solving Group Cheltenham An Infinite Product Based on a Base:
11222 . . . . . . . . . . . . . . . . . 465--466
Dietrich Trenkler and
Götz Trenkler and
Patrick Corn The Square Root of a Certain Matrix:
11224 . . . . . . . . . . . . . . . . . 466--467
Cezar Lupu and
Tudorel Lupu and
Ronald A. Kopas A New Bound for r/R: 11245 . . . . . . . 467--468
Paolo Perfetti and
Richard Stong Evaluate the Series: 11260 . . . . . . . 468--468
Ranjan Roy Book Review: \booktitleEuler Through
Time: A New Look at Old Themes, by V. S.
Varadarajan . . . . . . . . . . . . . . 469--473
Mark E. Kidwell Book Review: \booktitleKing of Infinite
Space: Donald Coxeter, the Man Who Saved
Geometry, by Siobhan Roberts . . . . . . 474--476
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Andrew M. Baxter and
Ronald Umble Periodic Orbits for Billiards on an
Equilateral Triangle . . . . . . . . . . 479--491
Niklas Eriksen The Freshman's Approach to Conway's
Napkin Problem . . . . . . . . . . . . . 492--498
Shlomo Engelberg Edge Detection Using Fourier
Coefficients . . . . . . . . . . . . . . 499--513
Sayel A. Ali The mth Ratio Test: New Convergence
Tests for Series . . . . . . . . . . . . 514--524
Thomas Schmelzer and
Robert Baillie Summing a Curious, Slowly Convergent
Series . . . . . . . . . . . . . . . . . 525--540
Daniel Birmajer and
Juan B. Gil Arithmetic in the Ring of Formal Power
Series with Integer Coefficients . . . . 541--549
Wouter Castryck A Shortened Classical Proof of the
Quadratic Reciprocity Law . . . . . . . 550--551
Rajendra Bhatia and
J. A. Dias da Silva Infinite Divisibility of GCD Matrices 551--553
Alexey Yu. Volovikov Borsuk--Ulam Implies Brouwer: a Direct
Construction Revisited . . . . . . . . . 553--556
George Koumoullis On the Radon--Nikodym Theorem . . . . . 556--558
William M. Kantor Cycles in Graphs and Groups . . . . . . 559--562
Michael D. Hirschhorn A Letter from Fitzroy House . . . . . . 563--566
Donald Knuth Problem 11369 . . . . . . . . . . . . . 567--567
Michael Goldenberg and
Mark Kaplan Problem 11370 . . . . . . . . . . . . . 567--567
Ovidiu Furdui Problem 11371 . . . . . . . . . . . . . 567--568
Jennifer Vandenbussche and
Douglas B. West Problem 11372 . . . . . . . . . . . . . 568--568
Emeric Deutsch Problem 11373 . . . . . . . . . . . . . 568--568
Harley Flanders and
Hugh L. Montgomery Problem 11374 . . . . . . . . . . . . . 568--568
Cezar Lupu Problem 11375 . . . . . . . . . . . . . 568--568
Syrous Marivani and
Missouri State University Problem Solving Group Consecutive Squares with a Square
Average: 11227 . . . . . . . . . . . . . 568--569
Isaac Sofair and
C. R. Pranesachar Inscribed Triangle Area: 11261 . . . . . 569--571
Hervé Moulin A Combinatorial Inequality: 11269 . . . 571--573
Vasile Mihai and
Sin Hitotumatu The Euler Line after All: 11272 . . . . 573--574
Jeffrey D. Vaaler Book Review: \booktitleAn Invitation to
Modern Number Theory, by Steven J.
Miller; Bamin Takloo-Bighash . . . . . . 575--578
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Wolfhard Hansen A Strong Version of Liouville's Theorem 583--595
Patrick D. McSwiggen and
Kenneth R. Meyer Conjugate Phase Portraits of Linear
Systems . . . . . . . . . . . . . . . . 596--614
Kenneth Hicks and
Gary L. Mullen and
Joseph L. Yucas and
Ryan Zavislak A Polynomial Analogue of the 3n + 1
Problem . . . . . . . . . . . . . . . . 615--622
Mehrdad Khosravi and
Michael D. Taylor The Wedge Product and Analytic Geometry 623--644
Stan Wagon and
Peter Webb Venn Symmetry and Prime Numbers: a
Seductive Proof Revisited . . . . . . . 645--648
Harald Hanche-Olsen On Goursat's Proof of Cauchy's Integral
Theorem . . . . . . . . . . . . . . . . 648--652
Arnaud Bodin Number of Irreducible Polynomials in
Several Variables over Finite Fields . . 653--660
Stefan Schröer Baer's Result: The Infinite Product of
the Integers Has No Basis . . . . . . . 660--663
Bogdan M. Baishanski Problem 11376 . . . . . . . . . . . . . 664--664
Christopher Hillar and
Lionel Levine Problem 11377 . . . . . . . . . . . . . 664--664
Daniel Troy Problem 11378 . . . . . . . . . . . . . 664--664
Oskar Maria Baksalary and
Götz Trenkler Problem 11379 . . . . . . . . . . . . . 664--664
Hugh Montgomery and
Harold S. Shapiro Problem 11380 . . . . . . . . . . . . . 665--665
Jesús Guillera and
Jonathan Sondow Problem 11381 . . . . . . . . . . . . . 665--665
Roberto Tauraso Problem 11382 . . . . . . . . . . . . . 665--665
Christopher J. Hillar and
O. P. Lossers A Group In Which Equations Are Solvable:
11231 . . . . . . . . . . . . . . . . . 665--666
Lenny Jones and
Rachel Keller and
Toni Ernvall and
Anne-Maria Ernvall-Hytönen A Special Prime: 11235 . . . . . . . . . 666--666
Emeric Deutsch and
John H. Smith and
Albert Stadler An Equality for Parts in Partitions of
n: 11237 . . . . . . . . . . . . . . . . 666--667
Aviezri S. Fraenkel Sequences Built from the Golden Ratio:
11238 . . . . . . . . . . . . . . . . . 667--668
Donald Knuth and
Robin Chapman and
Reiner Martin Perfect Parity Patterns: 11243 . . . . . 668--670
Michael S. Becker and
David Beckwith and
Hongwei Chen Double Integral with Log and Sinh: 11275 670--671
Said Amghibech and
Joanna Chachulska and
Wojciech Matysiak A Matrix Inequality: 11296 . . . . . . . 671--671
Donald G. Saari Book Review: \booktitleThe Three Body
Problem, by Mauri Valtonen; Hannu
Karrunen . . . . . . . . . . . . . . . . 672--676
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
D. Minda and
S. Phelps Triangles, Ellipses, and Cubic
Polynomials . . . . . . . . . . . . . . 679--689
Rémi Langevin and
Pewel G. Walczak Holomorphic Maps and Pencils of Circles 690--700
Andrew Bashelor and
Amy Ksir and
Will Traves Enumerative Algebraic Geometry of Conics 701--728
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-Eighth William Lowell Putnam
Mathematical Competition . . . . . . . . 729--739
Steven J. Miller A Probabilistic Proof of Wallis's
Formula for $ \pi $ . . . . . . . . . . 740--745
Mikael Passare How to Compute $ \sum 1 / n^2 $ by
Solving Triangles . . . . . . . . . . . 745--752
Remco van der Hofstad and
Michael Keane An Elementary Proof of the Hitting Time
Theorem . . . . . . . . . . . . . . . . 753--756
Michael Nyblom Problem 11383 . . . . . . . . . . . . . 757--757
Moubinool Omarjee Problem 11384 . . . . . . . . . . . . . 757--757
José Luis Díaz-Barrero Problem 11385 . . . . . . . . . . . . . 757--757
Greg Markowsky Problem 11386 . . . . . . . . . . . . . 757--757
Oskar Maria Baksalary Problem 11387 . . . . . . . . . . . . . 758--758
M. Farrokhi Problem 11388 . . . . . . . . . . . . . 758--758
Elizabeth R. Chen and
Jeffrey C. Lagarias Problem 11389 . . . . . . . . . . . . . 758--758
Prithwijit De and
E. Omey Recalling 11159 and Sixty-Sixth Putnam
A5: 11277 . . . . . . . . . . . . . . . 758--759
Slavko Simic and
John H. Lindsey II Entire Limit: 11278 . . . . . . . . . . 759--759
Vitaly Stakhovsky Sliding Beads: 11279 . . . . . . . . . . 759--760
Harris Kwong and
GCHQ Problem Solving Group What We Mean, Not What We Say: 11280 . . 760--761
Yakub Aliyev and
Apostolis Demis and
Apostolis Denis and
The GCHQ Problem Solving Group A Triangular Result: 11285 . . . . . . . 761--762
Stephen J. Herschkorn and
BSI Problems Group Continuous Blackjack: 11287 . . . . . . 762--764
Oleh Faynshteyn and
Marian Tetival Formulas Involving the Angles of a
Triangle: 11289 . . . . . . . . . . . . 764--764
Daniel T. Kaplan Book Review: \booktitleGoogle's PageRank
and Beyond: The Science of Search Engine
Rankings, by Amy N. Langville; Carl D.
Meyer . . . . . . . . . . . . . . . . . 765--768
Jeffrey Lagarias and
Colin Mallows and
Allan Wilks and
Daniel J. Velleman Editor's Endnotes . . . . . . . . . . . 769--770
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Steven G. Krantz Complex Analysis as Catalyst . . . . . . 775--794
Tom M. Apostol and
Mamikon A. Mnatsakanian New Descriptions of Conics via Twisted
Cylinders, Focal Disks, and Directors 795--812
William W. Hackborn Projectile Motion: Resistance Is Fertile 813--819
Eugen J. Ionascu and
Dan Pritikin and
Stephen E. Wright $k$-Dependence and Domination in Kings
Graphs . . . . . . . . . . . . . . . . . 820--836
Ed Scheinerman and
Christian Blatter Four Shots for a Convex Quadrilateral 837--843
Reinhard Michel The (n + 1)th Proof of Stirling's
Formula . . . . . . . . . . . . . . . . 844--845
Bent Fuglede A Sharpening of Wielandt's
Characterization of the Gamma Function 845--850
Jesús Guillera Easy Proofs of Some Borwein Algorithms
for $ \pi $ . . . . . . . . . . . . . . 850--854
Jeffrey C. Lagarias Problem 11390 . . . . . . . . . . . . . 855--855
Marian Tetiva Problem 11391 . . . . . . . . . . . . . 855--855
Omran Kouba Problem 11392 . . . . . . . . . . . . . 855--855
Cosmin Pohoata Problem 11393 . . . . . . . . . . . . . 856--856
K. S. Bhanu Problem 11394 . . . . . . . . . . . . . 856--856
M. Farrokhi Problem 11395 . . . . . . . . . . . . . 856--856
Gérard Letac Problem 11396 . . . . . . . . . . . . . 856--856
Gregory Keselman and
Aleksandar Ili\'c and
O. P. Lossers Generalizing $ (1 - 1)^n = 0 $: 11230 856--857
Michel Bataille and
John W. Hagood If AB Preserves A, then BA Preserves B:
11239 . . . . . . . . . . . . . . . . . 857--858
Roberto Tauraso and
O. P. Lossers Fibonacci Numbers and Tilling a Board
with Cuts: 11241 . . . . . . . . . . . . 858--859
David Beckwith and
Michael R. Avidon and
Li Zhou ``The Ballot Problem in Disguise'', in
Disguise: 11249 . . . . . . . . . . . . 859--860
David Beckwith and
Michel Bataille A Permanent Lower Bound: 11253 . . . . . 860--861
Lenny Jones and
Toni Ernvall Primes with Special Primitive Roots:
11254 . . . . . . . . . . . . . . . . . 861--861
Nobuhisa Abe and
Marian Tetiva Never a Square: 11259 . . . . . . . . . 862--862
Ashay Burungale and
Kenneth Schilling and
Christopher Carl Heckman Getting to Know You, Directly and
Indirectly: 11262 . . . . . . . . . . . 862--862
Peter Duren Book Review: \booktitlePrinceton
Lectures in Analysis, by Elias M. Stein;
Rami Shakarchi . . . . . . . . . . . . . 863--866
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Stephan C. Carlson The Quest for a Fuzzy Tychonoff Theorem 871--887
Robert Baillie and
David Borwein and
Jonathan M. Borwein Surprising Sinc Sums and Integrals . . . 888--901
Wolfgang Stadje The Maximum Average Gain in a Sequence
of Bernoulli Games . . . . . . . . . . . 902--910
Jack Bookman and
Susan L. Ganter and
Rick Morgan Developing Assessment Methodologies for
Quantitative Literacy: a Formative Study 911--929
Ed Scheinerman and
Thomas J. Pickett and
Ann Coleman Another Continued Fraction for $ \pi $ 930--933
Bakir Farhi A Curious Result Related to Kempner's
Series . . . . . . . . . . . . . . . . . 933--938
Andrei Vernescu The Summation of a Family of Series . . 939--943
Washek F. Pfeffer A Devil's Platform . . . . . . . . . . . 943--947
Grahame Bennett Problem 11397 . . . . . . . . . . . . . 948--948
Stanley Huang Problem 11398 . . . . . . . . . . . . . 948--948
Biaggi Ricceri Problem 11399 . . . . . . . . . . . . . 948--948
Paul Bracken Problem 11400 . . . . . . . . . . . . . 948--948
Marius Cavachi Problem 11401 . . . . . . . . . . . . . 949--949
Catalin Barboianu Problem 11402 . . . . . . . . . . . . . 949--949
Yaming Yu Problem 11403 . . . . . . . . . . . . . 949--949
Manuel Kauers and
Richard Stong A Telescoping Fibonacci Sum: 11258 . . . 949--950
Eugene Herman and
Mark D. Meyerson 3-D Rotations and Translations: 11276 950--950
M. L. Glasser and
O. P. Lossers A Sinh a Series: 11286 . . . . . . . . . 950--951
Cezar Lupu and
Kenneth F. Andersen A Variant Intermediate Value: 11290 . . 951--952
Stefano Siboni and
O. P. Lossers Double Integral: 11295 . . . . . . . . . 952--953
Marian Tetiva and
John H. Lindsey II A Tricky Minimum: 11297 . . . . . . . . 953--954
Anonymous Errata and End Notes for 2008 . . . . . 954--955
Ioannis Kontoyiannis Book Review: \booktitleInformation and
Complexity in Statistical Modeling, by
Jorma Rissanen . . . . . . . . . . . . . 956--960
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Anonymous Volume Information . . . . . . . . . . . ??
Judith V. Grabiner Why Did Lagrange ``Prove'' the Parallel
Postulate? . . . . . . . . . . . . . . . 3--18
Mike Paterson and
Uri Zwick Overhang . . . . . . . . . . . . . . . . 19--44
Larry Goldstein A Probabilistic Proof of the
Lindeberg--Feller Central Limit Theorem 45--60
José Ángel Cid and
Rodrigo López Pouso Does Lipschitz with Respect to $x$ Imply
Uniqueness for the Differential Equation
$ y^\prime = f(x, y) $ ? . . . . . . . . 61--66
Ed Scheinerman and
Anton R. Schep A Simple Complex Analysis and an
Advanced Calculus Proof of the
Fundamental Theorem of Algebra . . . . . 67--68
Natalia Casás Ferreño Yet Another Proof of the Irrationality
of $ \sqrt 2 $ . . . . . . . . . . . . . 68--69
Giovanni Panti A General Lagrange Theorem . . . . . . . 70--74
Romeo Me\vstrovi\'c A Note on the Congruence $ \left
({\array {cc} n & d \\ . . . . . . . . . 75--77
Sheldon M. Ross A Simple Solution to a Multiple Player
Gambler's Ruin Problem . . . . . . . . . 77--81
Raimond Struble Problem 11404 . . . . . . . . . . . . . 82--82
Ovidiu Furdui Problem 11405 . . . . . . . . . . . . . 82--82
A. A. Dzhumadi\'ldaeva Problem 11406 . . . . . . . . . . . . . 82--82
Erwin Just Problem 11407 . . . . . . . . . . . . . 82--82
Marius Cavachi Problem 11408 . . . . . . . . . . . . . 83--83
Paolo Perfetti Problem 11409 . . . . . . . . . . . . . 83--83
Omran Kouba Problem 11410 . . . . . . . . . . . . . 83--83
Richard Jerrard and
John Wetzel and
Mark D. Meyerson A Solid with the Rupert Property: 11291 83--84
Pablo Fern\`andez Refolio and
Timothy Achenbach An Infinite Product: 11299 . . . . . . . 84--84
Ulrich Abel A Bernstein Polynomial Integral: 11300 84--85
Finbarr Holland and
Byoung Tae Bae A Quartic Inequality:- 11301 . . . . . . 85--86
Horst Alzer A Series with Harmonic Numbers: 11302 86--87
Teodora-Liliana R\vadulescu Signed Series Terms: 11304 . . . . . . . 87--88
Alexandru Rosoiu and
Victor Pambuccian An Inequality for Triangles: 11306 . . . 88--89
Erik Talvila Book Review: \booktitleA Garden of
Integrals, by Frank E. Burk . . . . . . 90--94
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Thomas L. Bartlow and
David E. Zitarelli Who Was Miss Mullikin? . . . . . . . . . 99--114
Tom M. Apostol and
Mamikon A. Mnatsakanian A New Look at the So-Called Trammel of
Archimedes . . . . . . . . . . . . . . . 115--133
Frank Morgan Manifolds with Density and Perelman's
Proof of the Poincaré Conjecture . . . . 134--142
Joseph Bak and
Pisheng Ding Shape Distortion by Analytic Functions 143--150
Christian Haase and
Josef Schicho Lattice Polygons and the Number 2i + 7 151--165
Stephen K. Lucas Approximations to $ \pi $ Derived from
Integrals with Nonnegative Integrands 166--172
Juan Pablo Pinasco New Proofs of Euclid's and Euler's
Theorems . . . . . . . . . . . . . . . . 172--174
Janusz Januszewski A Note on Covering a Square of Side
Length $ 2 + \varepsilon $ with Unit
Squares . . . . . . . . . . . . . . . . 174--178
Alun Wyn-jones Problem 11411 . . . . . . . . . . . . . 179--179
Omran Kouba Problem 11412 . . . . . . . . . . . . . 179--179
Mihály Bencze Problem 11413 . . . . . . . . . . . . . 179--179
Marian Tetiva Problem 11414 . . . . . . . . . . . . . 179--180
Finbar Holland Problem 11415 . . . . . . . . . . . . . 180--180
Yaming Yu Problem 11416 . . . . . . . . . . . . . 180--180
Cezar Lupu Problem 11417 . . . . . . . . . . . . . 180--180
Steve Butler and
Jia Mao Graphs with Few Edges, All in Short
Cycles: 11265 . . . . . . . . . . . . . 180--181
Marian Tetiva and
Robin Chapman Partitioning Values of a Polynomial into
Sets of Equal Sum: 11266 . . . . . . . . 181--183
Eugene A. Herman and
Richard Stong Commuting Transformations: 11267 . . . . 183--183
Ovidiu Furdui and
Vitaly Stakhovsky An Inequality with Trig: 11308 . . . . . 183--184
Roman Witu\la and
Damian S\lta and
Arman Darbinyan and
David Borwein A Trig-Of-Trig Inequality: 11309 . . . . 184--185
Stephen J. Herschkorn A Game with Coins and Balls: 11311 . . . 185--186
V. S. Varadarajan Book Review: \booktitleIntroduction to
Calculus and Classical Analysis, by Omar
Hijab . . . . . . . . . . . . . . . . . 187--190
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Barbara Faires Yueh-Gin Gung and Dr. Charles Y. Hu
Award for 2009 to Robert E. Megginson
for Distinguished Service to Mathematics 195--196
Alan H. Schoenfeld Working with Schools: The Story of a
Mathematics Education Collaboration . . 197--217
Russell A. Gordon Some Integrals Involving the Cantor
Function . . . . . . . . . . . . . . . . 218--227
Jerzy Kocik and
Andrzej Solecki Disentangling a Triangle . . . . . . . . 228--237
Aaron Melman Overshooting Properties of Newton-Like
and Ostrowski-Like Methods . . . . . . . 238--250
Serge Troubetzkoy Dual Billiards, Fagnano Orbits, and
Regular Polygons . . . . . . . . . . . . 251--260
Shirley Llamado Yap The Poincaré Lemma and an Elementary
Construction of Vector Potentials . . . 261--267
Emmanuel Preissmann and
Maurice Mischler Seating Couples around the King's Table
and a New Characterization of Prime
Numbers . . . . . . . . . . . . . . . . 268--272
Amir Akbary and
Zachary Friggstad Superabundant Numbers and the Riemann
Hypothesis . . . . . . . . . . . . . . . 273--275
George Lamb Problem 11418 . . . . . . . . . . . . . 276--276
Vasile Mihai Problem 11419 . . . . . . . . . . . . . 276--276
Kent Holing Problem 11420 . . . . . . . . . . . . . 277--277
Sergio Falcón and
Ángel Plaza Problem 11421 . . . . . . . . . . . . . 277--277
Christopher Hillar Problem 11422 . . . . . . . . . . . . . 277--277
Gregory Minton Problem 11423 . . . . . . . . . . . . . 277--277
Emeric Deutsch Problem 11424 . . . . . . . . . . . . . 277--277
Donald Knuth and
Richard Stong Reversal by Swaps: 11264 [2007, 77] . . 277--278
Cezar Lupu and
Li Zhou From Integral to Derivative: 11313
[2007, 744] . . . . . . . . . . . . . . 279--279
Yakub Aliyev and
Marian Tetiva A Floor Equation: 11314 [2007, 744] . . 279--281
Ovidiu Furdui and
National Security Agency Problems Group Convergence of an Improper Integral with
Three Parameters: 11316 [2007, 745] . . 281--283
David Beckwith and
GCHQ Problem Solving Group Sum of Digits: 11319 [2008, 835] . . . . 283--283
Philip D. Straffin Book Review: \booktitleMr. Hopkins' Men:
Cambridge Reform and British Mathematics
in the 19th Century, by Alex D. D. Craik 284--288
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Michael F. Barnsley Transformations between Self-Referential
Sets . . . . . . . . . . . . . . . . . . 291--304
B. Ross Barmish and
Nigel Boston Risk and Return Considerations in ``The
Weakest Link'' . . . . . . . . . . . . . 305--315
H. Fejzi\'c and
C. Freiling and
D. Rinne Descartes' Rule of Signs, Alternations
of Data Sets, and Balanced Differences 316--327
D. Drinen and
K. G. Kennedy and
W. M. Priestley An Optimization Problem with a
Surprisingly Simple Solution . . . . . . 328--341
Ethan D. Bloch A Simple Proof of a Generalized No
Retraction Theorem . . . . . . . . . . . 342--350
Bruce Solomon Central Cross-Sections Make Surfaces of
Revolution Quadric . . . . . . . . . . . 351--355
Idris D. Mercer On Furstenberg's Proof of the Infinitude
of Primes . . . . . . . . . . . . . . . 355--356
J. J. Koliha Mean, Meaner, and the Meanest Mean Value
Theorem . . . . . . . . . . . . . . . . 356--361
Giedrius Alkauskas A Curious Proof of Fermat's Little
Theorem . . . . . . . . . . . . . . . . 362--364
Erwin Just Problem 11425 . . . . . . . . . . . . . 365--365
M. L. Glasser Problem 11426 . . . . . . . . . . . . . 365--365
Viorel B\vandil\va Problem 11427 . . . . . . . . . . . . . 365--365
Walter Blumberg Problem 11428 . . . . . . . . . . . . . 365--365
Cezar Lupu Problem 11429 . . . . . . . . . . . . . 365--366
He Yi Problem 11430 . . . . . . . . . . . . . 366--366
Finbarr Holland and
Stephen Wills Problem 11431 . . . . . . . . . . . . . 366--366
Marian Tetiva and
Robin Chapman Partitioning Values of a Polynomial into
Sets of Equal Sum: 11266 [2007, 77] . . 366--368
Sergey Sadov and
Harris Kwong The Determinant of a Spiral Matrix:
11270 [2007, 78] . . . . . . . . . . . . 368--369
Iliya Bluskov Covering the Chessboard with Sets of
Non-Attacking Queens: 11271 [2007, 164] 369--370
Sergey Sadov and
Kim McInturff and
Santa Barbara Determinant of Another Spiral Matrix:
11293 [2007, 451] . . . . . . . . . . . 370--371
Jakob Jonsson and
Annie Carter and
David Callan Oddly Triangulated Polygons: 11298
[2007, 547] . . . . . . . . . . . . . . 371--372
M. Farrokhi and
T. S. Michael A Characterization of Permutation
Matrices: 11303 [2007, 548] . . . . . . 372--372
James W. Vick Book Review: \booktitleTopology Now!, by
Robert Messer; Philip Straffin;
Introduction to Topology: Pure and
Applied ~by Colin Adams; Robert Franzosa 373--375
Kristopher Tapp Book Review: \booktitleDifferential
Geometry and Its Applications, by John
Oprea . . . . . . . . . . . . . . . . . 375--377
Daniel J. Velleman Editor's Endnotes . . . . . . . . . . . 378--382
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Jonathan M. Borwein and
Neil J. Calkin and
Dante Manna Euler--Boole Summation Revisited . . . . 387--412
Mira Bhargava Groups as Unions of Proper Subgroups . . 413--422
Rick Mabry and
Paul Deiermann Of Cheese and Crust: a Proof of the
Pizza Conjecture and Other Tasty Results 423--438
Nieves Alamo and
Carlos Criado Parallel Transport and Thomas--Wigner
Rotation . . . . . . . . . . . . . . . . 439--446
Daniel Heath and
I. M. Isaacs and
John Kiltinen and
Jessica Sklar Symmetric and Alternating Groups
Generated by a Full Cycle and Another
Element . . . . . . . . . . . . . . . . 447--451
Michael J. Evans and
Paul D. Humke Revisiting a Century-Old
Characterization of Baire Class One,
Darboux Functions . . . . . . . . . . . 451--455
Chris Bernhardt A Proof of the Cayley--Hamilton Theorem 456--457
Peter Wagner A New Constructive Proof of the
Malgrange--Ehrenpreis Theorem . . . . . 457--462
Marian Tetiva Problem 11432 . . . . . . . . . . . . . 463--463
Marius Cavachi Problem 11433 . . . . . . . . . . . . . 463--463
Slavko Simic Problem 11434 . . . . . . . . . . . . . 463--463
Panagiote Ligouras Problem 11435 . . . . . . . . . . . . . 463--463
Y. N. Aliyev Problem 11436 . . . . . . . . . . . . . 463--464
Tomás Erdélyi Problem 11437 . . . . . . . . . . . . . 464--464
David H. Bailey Problem 11438 . . . . . . . . . . . . . 464--464
Marian Tetiva and
Byron Schmuland A Sequence of Partitions into Sets with
Equal Sum: 11273 [2007, 164] . . . . . . 464--465
Max Alekseyev and
John Henry Steelman Counting Permutations with Two
Displacement Values: 11281 [2007, 259] 465--465
John Abbot and
John Wilkinson Irreducible Polynomials from a Theorem
of Fermat: 11283 [2007, 260] . . . . . . 465--466
Greg Oman and
Manuel Reyes Rings That are Fields: 11284 [2007, 358] 466--466
Marc LeBrun Descending Dungeons: 11286 [2007, 358] 466--467
Christopher Hillar and
Said Amghibech A Polynomial Identity: 11288 [2007, 359] 468--468
David Callan and
Robin Chapman Divisibility of a Central Binomial Sum:
11292 & 11307 [2007, 451 & 640] . . . . . 468--470
M. Farrokhi and
Tuomas Hytönen The Prime Exponentiation of an Integer:
11315 [2007, 744] . . . . . . . . . . . 470--470
Allen Holder Book Review: \booktitleUnderstanding and
Using Linear Programming, by Ji\vrí
Matou\vsek; Bernd Gärtner; Introduction
to Optimization ~by Pablo Pedregal . . . 471--476
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Alissa S. Crans and
Thomas M. Fiore and
Ramon Satyendra Musical Actions of Dihedral Groups . . . 479--495
Julius B. Barbanel and
Steven J. Brams and
Walter Stromquist Cutting a Pie Is Not a Piece of Cake . . 496--514
Jack S. Calcut Gaussian Integers and Arctangent
Identities for $ \pi $ . . . . . . . . . 515--530
Kevin Beanland and
James W. Roberts and
Craig Stevenson Modifications of Thomae's Function and
Differentiability . . . . . . . . . . . 531--535
Ulrich Abel and
Mircea Ivan Over-Iterates of Bernstein's Operators:
a Short and Elementary Proof . . . . . . 535--538
Paul Levrie and
Walter Daems Evaluating the Probability Integral
Using Wallis's Product Formula for $ \pi
$ . . . . . . . . . . . . . . . . . . . 538--541
Gerald Kuba Counting Fields of Complex Numbers . . . 541--546
Stephen Herschkorn Problem 11439 . . . . . . . . . . . . . 547--547
Stefano Siboni Problem 11440 . . . . . . . . . . . . . 547--547
Y. N. Aliyev Problem 11441 . . . . . . . . . . . . . 547--547
José Luis Díaz-Barrero and
José Gibergans-Báguena Problem 11442 . . . . . . . . . . . . . 547--548
Eugen Ionascu Problem 11443 . . . . . . . . . . . . . 548--548
Marian Tetiva Problem 11444 . . . . . . . . . . . . . 548--548
H. A. ShahAli Problem 11445 . . . . . . . . . . . . . 548--548
Donald Knuth and
Julian Hook Sums and Powers, Set Counting, and
Coefficient Tracking: 11274 [2007, 165] 548--549
Dragomir \vZ. \Dbarokovi\'c and
Richard Stong A Unipotent Matrix: 11282 [2007, 260] 549--550
Vahan Mkrtchyan and
Codrut Grosu Disjoint Maximum-Sized Matchings: 11305
[2007, 640] . . . . . . . . . . . . . . 550--551
Erwin Just and
Tom Kezlan An Exponential Condition for
Commutativity: 11310 [2007, 641] . . . . 551--552
David Callan and
Marc Renault Uniformly Distributed Valleys: 11312
[2007, 744] . . . . . . . . . . . . . . 552--553
Michel Bataille and
John Cade From Quadrilateral to Trapezoid: 11317
[2007, 745] . . . . . . . . . . . . . . 553--554
Branko Grünbaum Book Review: \booktitleThe Symmetries of
Things, by John H. Conway; Heidi
Burgiel; Chaim Goodman-Strauss . . . . . 555--562
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Nayandeep Deka Baruah and
Bruce C. Berndt and
Heng Huat Chan Ramanujan's Series for $ 1 / \pi $: a
Survey . . . . . . . . . . . . . . . . . 567--587
Greg Martin and
Erick B. Wong Almost All Integer Matrices Have No
Integer Eigenvalues . . . . . . . . . . 588--597
Tom M. Apostol and
Mamikon A. Mnatsakanian New Insight into Cycloidal Areas . . . . 598--611
Richard Kenyon and
Peter Winkler Branched Polymers . . . . . . . . . . . 612--628
Shui-Hung Hou On a Theorem of Abel . . . . . . . . . . 629--630
Jonathan Sondow Ramanujan Primes and Bertrand's
Postulate . . . . . . . . . . . . . . . 630--635
Shawn Hedman and
David Rose Light Subsets of N with Dense Quotient
Sets . . . . . . . . . . . . . . . . . . 635--641
Juan Sabia and
Susana Tesauri The Least Prime in Certain Arithmetic
Progressions . . . . . . . . . . . . . . 641--643
Oliver Deiser A Simple Continuous Bijection from
Natural Sequences to Dyadic Sequences 643--646
Christopher Hillar Problem 11446 . . . . . . . . . . . . . 647--647
Ovidiu Furdui and
Campia Turzii Problem 11447 . . . . . . . . . . . . . 647--647
Wei-Dong Jiang Problem 11448 . . . . . . . . . . . . . 647--647
Michel Bataille Problem 11449 . . . . . . . . . . . . . 647--647
Cosmin Pohoata Problem 11450 . . . . . . . . . . . . . 647--647
Greg Oman Problem 11451 . . . . . . . . . . . . . 648--648
Donald Knuth Problem 11452 . . . . . . . . . . . . . 648--648
Roman Witula and
Damian Stota and
Szeged Problem Group `Fejéntaláltuka' An Iteration Convergence: 11318 [2007,
745] . . . . . . . . . . . . . . . . . . 648--649
Donald Knuth and
O. P. Lossers Solving a Recurrence by Binary
Expansion: 11320 [2007, 835] . . . . . . 649--649
Christopher Hillar and
Bruce S. Burdick and
Roger Williams Polynomials Not Associated with
Symmetric Matrices: 11321 [2007, 835] 649--650
Jonathan Sondow and
George Lamb Tucson A Double Integral: 11322 [2007, 835] . . 650--650
Jody M. Lockhart and
William P. Wardlaw and
O. P. Lossers On the Sum of Integer Powers of a
Matrix: 11323 [2007, 835] . . . . . . . 650--651
Martin Kochanski and
Richard Stong Measuring the Growth Rate of a Bernoulli
Polynomial: 11324 [2007, 836] . . . . . 651--653
Finbarr Holland and
Michael Vowe A Triangle Inequality from 1953: 11325
[2007, 836] . . . . . . . . . . . . . . 653--654
José Luis Díaz-Barrero and
Pál Péter Dályay A Problem Rescued from Incorrectness:
11326 [2007, 836] . . . . . . . . . . . 654--655
Rick Mabry and
Debbie Shepherd and
Kenneth Schilling A Chancy Function: 11327 [2007, 925] . . 655--656
Dmitris Vartziotis and
Michel Bataille Van Aubel's Theorem: 11328 [2007, 925] 656--656
Neil Falkner Book Review: \booktitleBasic Real
Analysis, by Anthony W. Knapp; Advanced
Real Analysis ~by Anthony W. Knapp . . . 657--664
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Zajj Daugherty and
Alexander K. Eustis and
Gregory Minton and
Michael E. Orrison Voting, the Symmetric Group, and
Representation Theory . . . . . . . . . 667--687
Steven V. Sam A Bijective Proof for a Theorem of
Ehrhart . . . . . . . . . . . . . . . . 688--701
J. Scott Provan Sudoku: Strategy versus Structure . . . 702--707
Michael Bukatin and
Ralph Kopperman and
Steve Matthews and
Homeira Pajoohesh Partial Metric Spaces . . . . . . . . . 708--718
Leonard F. Klosinski and
Gerald L. Alexanderson and
Loren C. Larson The Sixty-Ninth William Lowell Putnam
Mathematical Competition . . . . . . . . 719--726
Ezra Brown and
Nicholas Loehr Why Is $ {\rm PSL}(2, 7) \cong {\rm
GL}(3, 2) $? . . . . . . . . . . . . . . 727--732
David V. Feldman and
Daniel A. Klain Angles as Probabilities . . . . . . . . 732--735
Villö Csiszár Jump Home and Shift: An Acyclic
Operation on Permutations . . . . . . . 735--738
Hojoo Lee Ptolemy Meets Erd\Hos and Mordell Again 738--742
Anca I. Bonciocat and
Nicolae C. Bonciocat On the Irreducibility of Polynomials
with Leading Coefficient Divisible by a
Large Prime Power . . . . . . . . . . . 743--745
Michel Bataille Problem 11449 . . . . . . . . . . . . . 746--746
Richard Stanley Problem 11453 . . . . . . . . . . . . . 746--746
Azer Kerimov Problem 11454 . . . . . . . . . . . . . 746--746
Christian Blatter Problem 11455 . . . . . . . . . . . . . 746--746
Raymond Mortini Problem 11456 . . . . . . . . . . . . . 747--747
M. L. Glasser Problem 11457 . . . . . . . . . . . . . 747--747
Cezar Lupu Problem 11458 . . . . . . . . . . . . . 747--747
Pál Péter Dályay Problem 11459 . . . . . . . . . . . . . 747--747
T. Amdeberhan and
Victor H. Moll and
Hongwei Chen Two Log Gamma Integrals: 11329 [2007,
925] . . . . . . . . . . . . . . . . . . 747--748
Marian Tetiva and
João Guerreiro A New Lower Bound for the Sum of the
Altitudes: 11330 [2007, 925] . . . . . . 748--749
Marian Tetiva and
Peter Nüesch A Bisector Inequality: 11337 [2008, 71] 749--750
Ovidiu Furdui and
O. P. Lossers A Gamma Limit: 11338 [2008, 71] . . . . 750--750
Óscar Ciaurri and
Luz Roncal and
Nora Thornber Raindrops Flying from a Spinning
Umbrella: 11340 [2008, 72] . . . . . . . 750--752
Cezar Lupu and
Marian Tetiva An Application of Popovidu's Inequality:
11341 [2008, 166] . . . . . . . . . . . 752--753
Roger Cuculi\`ere and
Richard Stong A Functional Equation: 11345 [2008, 166] 753--753
Judy Holdener Book Review: \booktitleRoots to
Research: A Vertical Development of
Mathematical Problems, by Judith D.
Sally; Paul J. Sally, Jr. . . . . . . . 754--758
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Mike Paterson and
Yuval Peres and
Mikkel Thorup and
Peter Winkler and
Uri Zwick Maximum Overhang . . . . . . . . . . . . 763--787
Persi Diaconis and
Jason Fulman Carries, Shuffling, and an Amazing
Matrix . . . . . . . . . . . . . . . . . 788--803
Luis Verde-Star Rational Functions . . . . . . . . . . . 804--827
Theo de Jong Lagrange Multipliers and the Fundamental
Theorem of Algebra . . . . . . . . . . . 828--830
D. M. Einstein and
C. C. Heckman and
T. S. Norfolk On Sara's Dove Bar Habit . . . . . . . . 831--835
Bakir Farhi An Identity Involving the Least Common
Multiple of Binomial Coefficients and
Its Application . . . . . . . . . . . . 836--839
Valerio De Angelis Stirling's Series Revisited . . . . . . 839--843
Cosmin Pohoa\ct\va Problem 11460 . . . . . . . . . . . . . 844--844
Panagiote Ligouras Problem 11461 . . . . . . . . . . . . . 844--844
Nadezhda Alexandrova Problem 11462 . . . . . . . . . . . . . 844--844
Xiang Qian Chang Problem 11463 . . . . . . . . . . . . . 844--844
David Beckwith Problem 11464 . . . . . . . . . . . . . 845--845
Pantelimon George Popescu Problem 11465 . . . . . . . . . . . . . 845--845
Tian Yongge Problem 11466 . . . . . . . . . . . . . 845--845
Richard Bagby and
David Beckwith and
Sag Harbor and
Douglas B. Tyler A Weighted Sample of the Riemann Zeta
Function: 11331 [2007, 926] . . . . . . 845--846
Roberto Tauraso and
Kenneth Schilling Irrational Symmetry: 11332 [2007, 926] 846--847
Pablo Fernández Refolio and
John B. Zacharias Baking a Pi with Factorials: 11333
[2007, 926] . . . . . . . . . . . . . . 847--847
Jonathan Bober and
Jeffrey Lagarias and
Byron Schmuland Very Composite Numbers: 11334 [2008, 71] 847--848
Donald Knuth and
GCHQ Problem Solving Group Near-de Bruijn Cycles: 11336 [2008, 71] 848--849
Mihály Bencze and
Julien Grivaux More AGM Inequalities: 11347 [2008,167] 849--851
Victor J. Katz Book Review: \booktitleMathematical
Masterpieces: Further Chronicles by the
Explorers, by Arthur Knoebel; Reinhard
Laubenbacher; Jerry Lodder; David
Pengelley . . . . . . . . . . . . . . . 852--856
Daniel J. Velleman Editor's Endnotes . . . . . . . . . . . 857--858
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Peter D. Lax Rethinking the Lebesgue Integral . . . . 863--881
Reinhard Laubenbacher and
Bernd Sturmfels Computer Algebra in Systems Biology . . 882--891
Bob Palais and
Richard Palais and
Stephen Rodi A Disorienting Look at Euler's Theorem
on the Axis of a Rotation . . . . . . . 892--909
Bettina Richmond and
Tom Richmond How to Recognize a Parabola . . . . . . 910--922
Robert Beals On Orders of Subgroups in Abelian
Groups: An Elementary Solution of an
Exercise of Herstein . . . . . . . . . . 923--926
Alexander E. Holroyd and
Terry Soo A Nonmeasurable Set from Coin Flips . . 926--928
John Brillhart A Note on Euler's Factoring Problem . . 928--931
Joseph B. Keller and
Ravi Vakil $ \pi_p $, the Value of $ \pi $ in $
\ell_p $ . . . . . . . . . . . . . . . . 931--935
Lucio R. Berrone The Associativity of the Pythagorean Law 936--939
Xiang Qian Chang Problem 11467 . . . . . . . . . . . . . 940--940
Cosmin Pohoata Problem 11468 . . . . . . . . . . . . . 940--940
Slavko Simic Problem 11469 . . . . . . . . . . . . . 940--940
Marian Tetiva Problem 11470 . . . . . . . . . . . . . 941--941
Finbarr Holland Problem 11471 . . . . . . . . . . . . . 941--941
Mahdi Makhul Problem 11472 . . . . . . . . . . . . . 941--941
Paolo Perfetti Problem 11473 . . . . . . . . . . . . . 941--941
Juan López González and
O. P. Lossers Multiples of 6 Whose Successors Have
Greater Divisor Sum: 11335 [2008, 71] 941--942
José Luis Díaz-Barrero and
Mihai Cipu A Fibonacci Inequality: 11339 [2008, 72] 942--943
Luis H. Gallardo and
Sam Vandervelde A Square in a Finite Field: 11342 [2008,
166] . . . . . . . . . . . . . . . . . . 943--944
David Beckwith and
CMC 328 The Number of Balanced Senates from $n$
States: 11343 [2008, 166] . . . . . . . 944--945
Albert Stadler and
Allen Stenger A Möbius Function Identity: 11344 [2008,
166] . . . . . . . . . . . . . . . . . . 945--946
Anonymous Errata and End Notes for 2008 . . . . . 947--947
Michael Henle Book Review: \booktitleMusic: A
Mathematical Offering, by David J.
Benson; Musimathics: The Mathematical
Foundations of Music ~by Gareth Loy . . 948--955
Anonymous Back Matter . . . . . . . . . . . . . . ??
Anonymous Front Matter . . . . . . . . . . . . . . ??
Anonymous Volume Information . . . . . . . . . . . ??