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Anonymous Index to the \booktitleMathematical
Gazette . . . . . . . . . . . . . . . . i--ix
Anonymous MAG volume 94 issue 529--531 Cover and
Front matter . . . . . . . . . . . . . . f1--f1
Bill Richardson Doug French . . . . . . . . . . . . . . 1--4
Doug French and
David Jordan Dodecahedral slices and polyhedral
pieces . . . . . . . . . . . . . . . . . 5--17
Bob Burn Sums of powers of integers --- how
Fermat may have found them . . . . . . . 18--26
H. Matsui and
D. Minematsu and
T. Yamauchi and
R. Miy Adera Pascal-like triangles and Fibonacci-like
sequences . . . . . . . . . . . . . . . 27--41
Juan Pla A kaleidoscope of solutions for a
Diophantine system . . . . . . . . . . . 42--50
Vera L. X. Figueiredo and
Margarida P. Mello and
Sandra A. Santos Beyond domes, umbrellas and tents . . . 51--61
Thomas J. Osler Vieta-like products of nested radicals 62--66
Alasdair McAndrew An elementary, limit-free calculus for
polynomials . . . . . . . . . . . . . . 67--83
R. W. Smyth An interesting strategic blunder . . . . 84--93
John Mahony The polarisation ellipse and associated
properties . . . . . . . . . . . . . . . 94--102
J. A. Scott Miscellaneous triangle properties . . . 103--111
Bob Burn Chris Ormell's article . . . . . . . . . 112--113
Emrys Read 94.01 On digit transfers . . . . . . . . 114--117
S. B. Junaidu and
A. Laradji and
A. Umar 94.02 Powers of integers as sums of
consecutive odd numbers . . . . . . . . 117--119
G. J. O. Jameson 94.03 Two squares and four squares: the
simplest proof of all? . . . . . . . . . 119--123
G. J. O. Jameson 94.04 Even and odd square-free numbers 123--127
Paul Myer Kominers and
Scott Duke Kominers 94.05 Improved bounds on the sizes of S$
\cdot $P numbers . . . . . . . . . . . . 127--129
Peter Shiu 94.06 A footnote to Besicovitch's arc 130--132
Mitsuhiro Kumano 94.07 A generalisation of the limits of
certain sequences . . . . . . . . . . . 132--135
Russell Euler and
Jawad Sadek 94.08 A multiplicative-type property for
determinants . . . . . . . . . . . . . . 135--136
Alberto Zorzi 94.09 Lattice polygons and the number
12: an elementary proof . . . . . . . . 137--143
Michael O'Loughlin 94.10 Half angles and the inradius of a
Pythagorean triangle . . . . . . . . . . 144--146
Nick Lord Variations on a theme --- squares in a
circular sector . . . . . . . . . . . . 147--149
Barry Blight and
Mike Cornelius and
Nick Lord Finding an angle of rotation in
coordinate geometry . . . . . . . . . . 149--150
Anonymous Feedback . . . . . . . . . . . . . . . . 151--158
Nick Lord Problem Corner . . . . . . . . . . . . . 159--165
Tim Cross Student Problems . . . . . . . . . . . . 165--167
I. Grattan-Guinness Extended Review: \booktitleThe first
century of the International Commission
on Mathematical Instruction
(1908--2008). Reflecting and shaping the
world of mathematics education. M.
Menghini, F. Furinghetti, L. Giacardi
and F. Arzarello (eds.). Pp. 328. EUR60.
2008. ISBN: 978-88-12-00015-9 (Rome:
Istituto della Enciclopedia Italiana) 168--172
Hugh Williams Book Review: \booktitleSymmetry and the
monster: one of the greatest quests of
mathematics, by Mark Ronan. Pp. 272.
\pounds 8-99. 2006. ISBN:
978-0-19-280722-9 (Oxford University
Press) . . . . . . . . . . . . . . . . . 173--174
Michael De Villiers Book Review: \booktitleLeonhard Euler,
by Emil Fellmann. Pp. 179. \pounds 23.00
(Hardback). 2007. ISBN 13:
978-3-7643-7538-6 (Birkhäuser Verlag) . . 174--176
Bruce Roth Book Review: \booktitleEuler's gem, by
David S. Richeson. Pp. 336. \pounds
16.95. 2008. ISBN 978-0-691-12677-7
(Princeton University Press) . . . . . . 176--177
Martin Griffiths Book Review: \booktitleEmmy Noether: the
mother of modern algebra, by M. B. W.
Tent. Pp. 177. \$29. (Hardback). 2008.
ISBN 978-1-56881-430-8 (A. K. Peters)} 177--178
Peter Giblin Book Review: \booktitleThe unravelers,
mathematical snapshots, J.-F. Dars, A.
Lesne and A. Papillault, (eds) (trans.
V. Méla) \pounds 26.50. 2008. ISBN
978-1-56881-441-4 (A. K. Peters) . . . . 178--180
John Baylis Book Review: \booktitleThe magic numbers
of the professor, by Owen O'Shea and
Underwood Dudley. Pp. 168. \pounds
21.99. 2007. ISBN 0 88385 557 7 (The
Mathematical Association of America) . . 180--181
Piotr Zarzycki Book Review: \booktitleThe teaching
assistant's guide to numeracy, by Sara
Fielder. Pp. 117. \pounds 12.99. 2007.
ISBN 978-0-8264-9606-5 (Continuum) . . . 181--182
Graham H. Storr Book Review: \booktitleEven better
mathematics: looking back to move
forward, by Afzal Ahmed and Honor
Williams. Pp. 99. \pounds 19.99. 2007.
ISBN 978-1-85539-147-5 (Network
Continuum Education) . . . . . . . . . . 182--183
Peter Shiu Book Review: \booktitleExperimental
number theory, by Fernando Rodriguez
Villegas. Pp. 214. \pounds 31.00 (pbk).
2007. ISBN 978-0-19-922730-3 (Oxford
University Press) . . . . . . . . . . . 183--183
Peter Shiu Book Review: \booktitleExperimental
number theory, by Fernando Rodriguez
Villegas. Pp. 214. \pounds 31.00 (pbk).
2007. ISBN 978-0-19-922730-3 (Oxford
University Press) . . . . . . . . . . . 183--183
Ian Anderson Book Review: \booktitleAn introduction
to the theory of numbers (sixth
edition), by G. H. Hardy and E. M.
Wright. Pp. 620. 2008. \pounds 30
(paperback). ISBN: 978-0-19-921986-5
(Oxford University Press) . . . . . . . 184--184
Ian Anderson Book Review: \booktitleAn introduction
to the theory of numbers (sixth
edition), by G. H. Hardy and E. M.
Wright. Pp. 620. 2008. \pounds 30
(paperback). ISBN: 978-0-19-921986-5
(Oxford University Press) . . . . . . . 184--184
John Baylis Book Review: \booktitleThe backbone of
Pascal's triangle, by Martin Griffiths.
Pp. 163. \pounds 12.00. 2007. ISBN
978-1-906001-04-9 (The United Kingdom
Mathematics Trust) . . . . . . . . . . . 184--185
Philip Maher Book Review: \booktitlePractical linear
algebra: a geometry toolbox, by Gerald
Farin and Dianne Hansford. Pp. 384.
\pounds 56-00. 2005. ISBN: 1-56881-234-5
(A. K. Peters) . . . . . . . . . . . . . 185--187
Peter MacGregor Book Review: \booktitleFeedback systems:
an introduction for scientists and
engineers, by K. J. Åstrom and R. M.
Murray. Pp. 396. \pounds 26.95. 2008.
ISBN: 0-691-13576-2 (Princeton) . . . . 187--187
Piotr Zarzycki Book Review: \booktitleA Mathematical
Olympiad Primer, by Geoff Smith. Pp.
178. \pounds 10.00. 2008. ISBN
978-1-906001-03-2 (The United Kingdom
Mathematics Trust) . . . . . . . . . . . 187--188
Bruce Roth Book Review: \booktitleFlips for
$3$-folds and $4$-folds, Alessio Corti
(ed.). Pp. 200. \pounds 41.00. 2007.
ISBN 978-0-19-857061-5 (Oxford
University Press) . . . . . . . . . . . 188--189
Mary Fortune Book Review: \booktitleGeometric
Origami, by Robert Geretschläger. Pp.
198, \pounds 14.00. 2008. ISBN:
978-0-9555477-1-3 (Arbelos) . . . . . . 189--190
Gerry Leversha Book Review: \booktitleThe annotated
Flatland, by Edwin A. Abbott and Ian
Stewart. Pp. 242. \pounds 10.99. 2008.
ISBN 978-0-465-01123-0 (Basic Books) . . 190--191
Anonymous MAG volume 94 issue 529 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Anonymous MAG volume 94 issue 529 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Tony Crilly and
Colin R. Fletcher How to choose your relations . . . . . . 193--202
Michael Jewess Optimising the acceleration due to
gravity on a planet's surface . . . . . 203--215
J. Trainin Integrating expressions of the form $
\sin^n x / x^m $ and others . . . . . . 216--223
Mark Spahn and
Ron Lancaster and
Deborah Moore-Russo and
Gerald Rising An unexpected use of primes: solving
sudokus by calculator . . . . . . . . . 224--232
Tony Crilly and
Alan Pryor Rugby conversions: a $3$-dimensional
model . . . . . . . . . . . . . . . . . 233--238
Nick Lord and
John Rigby and
Douglas Quadling (The Bride's Chair)$^2$ . . . . . . . . 239--246
Peter Hilton and
Jean Pedersen Stop-sign theorems and binomial
coefficients . . . . . . . . . . . . . . 247--261
Juan Pla A footnote to the theory of double
integrals . . . . . . . . . . . . . . . 262--269
Alina S\^\intamarian Regarding a generalisation of
Ioachimescu's constant . . . . . . . . . 270--283
Michael Z. Spivey 94.11 Visualising continued fractions 284--290
Konstantine Zelator and
Ovidiu Furdui 94.12 The non-existence of integer
solutions to $ p y^2 = x^4 + x $ . . . . 290--294
B. Sury 94.13 Group theory lends a hand to
number theory . . . . . . . . . . . . . 294--296
Thomas P. Dence 94.14 On an identity involving binomial
coefficients via $ \arctan (x) $ . . . . 296--298
R. P. Burn 94.15 Napier's table of logarithms . . . 299--303
Scorr Duke Kominers 94.16 Irrational roots revisited . . . . 303--304
J. A. Scott 94.17 Evaluating the Euler constant . . 304--306
Ángel Plaza and
Sergio Falcón 94.18 Proof without words: Two
inequalities proved by convexity . . . . 306--308
Grzegorz Rzadkowski 94.19 A calculus-based approach to the
von Staudt--Clausen theorem . . . . . . 308--312
Nick Lord 94.20 An interesting constraint on
cutting corners . . . . . . . . . . . . 312--314
Anthony Sofo 94.21 Grandma, grandaunts and distant
cousins . . . . . . . . . . . . . . . . 314--316
Joe DeMaio 94.22 Proof without words:
decompositions of $ \binom {n + 1}{2} $
and $ n^2 $ . . . . . . . . . . . . . . 317--317
Tony Crilly 94.23 Handshaking across a table . . . . 317--321
Andrew Jobbings 94.24 Sudoku is four-dimensional . . . . 321--326
Anthony C. Robin 94.25 Binomial within binomial yields
binomial . . . . . . . . . . . . . . . . 327--330
Nick Lord Binomial averages when the mean is an
integer . . . . . . . . . . . . . . . . 331--332
Glyn George The integral of $ 1 / x $ . . . . . . . 332--334
Colin Foster Correspondence . . . . . . . . . . . . . 335--335
Nick Lord Correspondence . . . . . . . . . . . . . 335--336
Anonymous Feedback . . . . . . . . . . . . . . . . 336--341
N. J. L. Problem Corner . . . . . . . . . . . . . 342--349
Stan Dolan Student Problems . . . . . . . . . . . . 350--353
Anonymous In Memoriam . . . . . . . . . . . . . . 353--353
Kevin Davis Book Review: \booktitleCore C1 and C2: A
level mathematics for Edexcel, by Peter
Hind. Pp. 375. \pounds 19.50. 2008. ISBN
978-0-19-911779-6. (Oxford University
Press) . . . . . . . . . . . . . . . . . 355--355
Nick Lord Book Review: \booktitlePenguin
dictionary of mathematics (4th edn),
David Nelson (ed.). Pp. 480. \pounds
10.99. 2008. ISBN 978-0-14-103023-4
(Penguin) . . . . . . . . . . . . . . . 355--355
Bruce Roth Book Review: \booktitleDecision D1: A
Level mathematics for Edexcel, by Brian
Jefferson. Pp. 192. \pounds 10. 2008.
ISBN: 978-0-19-911780-2 (Oxford
University Press) . . . . . . . . . . . 356--356
Peter Hall Book Review: \booktitleStatistics S1: A
Level mathematics for Edexcel, by James
Nicholson. Pp. 223. \pounds 10.00. 2008.
ISBN: 978-0-19-911782-6 (Oxford
University Press) . . . . . . . . . . . 356--357
Peter MacGregor Book Review: \booktitleMathematical
techniques: an introduction for the
engineering, physical and mathematical
sciences (4th edn), by D. W. Jordan and
P. Smith. Pp. 976. \pounds 31.99. 2008.
ISBN 978-0-19-928201-2 (Oxford
University Press) . . . . . . . . . . . 357--358
Jennie Golding Book Review: \booktitleMechanics M1: A
Level mathematics for Edexcel, by Brian
Jefferson. Pp. 185. \pounds 10.00. 2008.
ISBN 978-0-19-911781-9 (Oxford
University Press) . . . . . . . . . . . 358--358
I. Grattan-Guinness Book Review: \booktitleMr Hopkins' men
--- Cambridge reform and British
mathematics in the 19th century, by A.
D. D. Craik. Pp. 405. 2007. \pounds
65.00. ISBN 978-1-84628-790-9 (Springer) 358--359
P. N. Ruane Book Review: \booktitleLewis Carroll in
Numberland. His fantastical mathematical
logical life, by Robin Wilson. pp. 237.
\pounds 16.99. 2008. ISBN
978-0-713-99757-6 (Allen Lane) . . . . . 359--360
Graham Hoare Book Review: \booktitleBenjamin
Franklin's numbers. An unsung
mathematical odyssey, by Paul C. Pasles.
pp. 254. \pounds 15.95. 2008. ISBN 13:
978-0-691-12956-3 (Princeton University
Press) . . . . . . . . . . . . . . . . . 360--361
Gerry Leversha Book Review: \booktitleThe unfinished
game, by Keith Devlin. pp. 170. \$24.95.
2008. ISBN 978-0-465-00910-7 (Basic
Books)} . . . . . . . . . . . . . . . . 361--362
Paul Hudson Book Review: \booktitleThe presidential
election game, by Steven J. Brams. pp.
194. \$29. 2008. ISBN 978-1-56881-348-6
(A. K. Peters)} . . . . . . . . . . . . 362--363
Gerry Leversha Book Review: \booktitleThe shape of
content: creative writing in mathematics
and science, Chandler Davis, Marjorie
Wikler Senechal and Jan Zwicky (eds.).
Pp. 194. \$39. 2008. ISBN
978-1-56881-444-5 (AK Peters).
\booktitle{Strange attractors: poems of
love and mathematics}, Sarah Glaz and
JoAnne Growney (eds.). Pp 255. \$39.
2008. ISBN 978-1-56881-341-7 (AK Peters) 363--364
Michael Ward Book Review: \booktitle50 mathematical
ideas you really need to know, by Tony
Crilly. pp. 208. \pounds 8.99. 2008.
ISBN 978-1-84724-008-8 (Quercus
Publishing plc) . . . . . . . . . . . . 365--365
Alan Sutcliffe Book Review: \booktitleLegacy of the
Luoshu: the 4,000 year search for the
meaning of the magic square of order
three (2nd edn), by Frank J. Swetz. Pp.
214. \pounds 21.50 (hardback). 2008.
ISBN 978 1 56881 427 8 (A. K. Peters) 365--367
Gerry Leversha Book Review: \booktitle50 mathematical
ideas you really need to know, by Tony
Crilly. Pp. 208. \pounds 8.99. 2008.
ISBN 977-1-84724-008-8 (Quercus) . . . . 367--368
Doug French Book Review: \booktitleAssessing
mathematical proficiency, Alan H.
Schoenfeld (ed.). Pp. 391. \pounds
17.99. 2007. ISBN 0521 69766 8
(Cambridge University Press) . . . . . . 368--369
Gerry Leversha Book Review: \booktitleHow to think like
a mathematician, by Kevin Houston. Pp.
265. \pounds 18.99. 2009. ISBN
978-0-521-71978-0 (CUP) . . . . . . . . 369--371
Doug French Book Review: \booktitleThirty three ways
to help with numeracy, by Brian Sharp.
Pp. 124. \pounds 19.99. 2009. ISBN 9 78
0415 46896 1 (David Fulton) . . . . . . 371--371
David Applebaum Book Review: \booktitleAdvanced
calculus: an introduction to linear
analysis, by Leonard F. Richardson, J.
Wiley and Sons, Inc. (2008), ISBN:
978-0-470-23288-0 \pounds 78.50, \$97.50
(hbk) pp. 387} . . . . . . . . . . . . . 372--373
Peter Shiu Book Review: \booktitleA first course in
functional analysis, by S. David
Promislow. Pp. 307. \pounds 52.95
(hardback). 2008. ISBN:
978-0-470-14619-7 (Wiley) . . . . . . . 373--373
Peter Shiu Book Review: \booktitleTopics in Galois
theory (2nd edn), by Jean-Pierre Serre.
Pp. 120. \$39.00. 2008. ISBN
978-1-56881-412-4 (A. K. Peters)} . . . 374--374
John Baylis Book Review: \booktitleHexaflexagons,
probability paradoxes and the tower of
Hanoi: Martin Gardner's first book of
mathematical puzzles and games, by
Martin Gardner. Pp. 193. \pounds 8-99.
2008. ISBN 978-0-521-73525-4 (Cambridge
University Press) . . . . . . . . . . . 375--375
Nick Lord Book Review: \booktitleClassical
algebra, by Roger Cooke. Pp. 206.
\pounds 28.95. 2008. ISBN 978 0 470
25952 8 (Wiley) . . . . . . . . . . . . 375--376
S. C. Coutinho Book Review: \booktitleFrom quantum
cohomology to integrable systems, by
Martin A. Guest. Oxford Graduate Texts
in Mathematics. Pp. 328. \$45.00
(hardback). 2008. ISBN 13:
978-0-19-856599-4 (Oxford University
Press)} . . . . . . . . . . . . . . . . 376--378
Mary Fortune Book Review: \booktitleMaking
mathematics with needlework, Sarah-Marie
Belcastro and Carolyn Yackel (eds). Pp.
184. \pounds 18.50. 2008. ISBN
978-1-56881-331-8 (A. K. Peters) . . . . 378--379
P. MacGregor Book Review: \booktitleMathematical
modeling and simulation, introduction
for scientists and engineers, by Kai
Velten. Pp. 348. \pounds 70.00. 2009.
ISBN: 978-3-527-40758-8 (Wiley-VCH) . . 379--380
Imre Leader Book Review: \booktitleProblems from the
Book, by Titu Andreescu and Gabriel
Dospinescu. Pp. 554. \$69.95. 2008. ISBN
978-0-9799269-0-7 (XYZ Press)} . . . . . 380--381
Owen Toller Book Review: \booktitleProfessor
Stewart's cabinet of mathematical
curiosities, by Ian Stewart. Pp. 256.
\pounds 10.99. 2008. ISBN
978-1-84668-064-9 (Basic Books (NY),
Profile Books Ltd (UK)) . . . . . . . . 381--381
C. W. Kilmister Book Review: \booktitleExotic infinity
and a long decline of confidence in
mathematics, Christopher Ormell. pp. 55.
2008. ISBN 0-907669-46-8
(Ingleside-Ashby for the PER Group) . . 381--382
Michael Ward Book Review: \booktitleInvariant
descriptive set theory, by Su Gao. Pp.
383. \pounds 49.99. 2008. ISBN
978-1-58488-793-5 (Chapman and Hall) . . 383--383
Anonymous MAG volume 94 issue 530 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 94 issue 530 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Jane Imrie Progressing through mathematics . . . . 386--400
Robert Edward Lewand The perfect cipher . . . . . . . . . . . 401--411
John Baylis Codes, not ciphers . . . . . . . . . . . 412--425
J. R. Harris Forming groups with 4 $ \times $ 4
matrices . . . . . . . . . . . . . . . . 426--429
Thomas J. Osler The tables of John Wallis and the
discovery of his product $ \pi $ . . . . 430--437
M. J. Englefield and
G. E. Farr Eigencircles and associated surfaces . . 438--449
Burkard Polster and
Marty Ross Mathematical Rugby . . . . . . . . . . . 450--463
Kung-Wei Yang 94.26 Computing quadratic fundamental
units . . . . . . . . . . . . . . . . . 464--467
Hang Chen and
Curtis Cooper 94.27 To your hearts' content . . . . . 467--473
Gareth Boreland 94.28 The hyperexponential function . . 473--476
Jacek Fabrykowski and
Thomas Smotzer 94.29 On two properties of the inverse
Hilbert matrix . . . . . . . . . . . . . 476--479
Timothy G. Feeman and
Osvaldo Marrero 94.30 Ratios of volumes related to the
odd extension of a power function . . . 479--486
Des MacHale 94.31 Approximations for $ \pi $ and $e$ 486--488
Rasul A. Khan 94.32 The recursive nature of Euler's
formula for harmonic series . . . . . . 488--492
A. McD. Mercer 94.33 Short proofs of Jensen's and
Levinson's Inequalities . . . . . . . . 492--495
Jeremy D. King 94.34 Regular polygons with integer
coordinates . . . . . . . . . . . . . . 495--498
Mowaffaq Hajja 94.35 Popularising the ASS
pseudo-congruence theorem . . . . . . . 499--502
Victor Bryant and
John Duncan 94.36 Wheels within wheels . . . . . . . 502--505
Martin Griffiths 94.37 Multinomial distributions and
knockout tournaments . . . . . . . . . . 505--509
Yves Nievergelt 94.38 The truth table of the logical
implication . . . . . . . . . . . . . . 509--513
Tony Barnard 94.39 An unlikely certainty . . . . . . 514--517
Stuart Simons 94.40 Getting to the centre . . . . . . 517--521
T. Nigel Lucas Obtaining derivatives of trigonometric
functions using mechanics . . . . . . . 522--526
Nick Lord A power series graphing challenge . . . 527--528
John R. Silvester C. W. Kilmister 1924--2010 . . . . . . . 529--531
Tony Gardiner William Salisbury Wynne Willson
1932--2010 . . . . . . . . . . . . . . . 532--534
Tony Crilly and
Colin R. Fletcher Correspondence . . . . . . . . . . . . . 535--535
Juan Pla Correspondence . . . . . . . . . . . . . 536--536
Anonymous Feedback . . . . . . . . . . . . . . . . 536--543
N. J. L. Problem Corner . . . . . . . . . . . . . 544--550
Stan Dolan Student Problems . . . . . . . . . . . . 551--552
Peter Hall Book Review: \booktitleGCSE revision
plus Edexcel maths revision guide,
edited by John Proctor, Tina Foster and
Rebecca Skinner. Pp. 120. \pounds 5-99.
2008. ISBN: 978-1-844191-91-8 (Letts and
Lonsdale) . . . . . . . . . . . . . . . 553--553
Peter J. Giblin Book Review: \booktitleThe map of my
life, by Goro Shimura. pp. 211, \pounds
19.99 (hardback). 2008. ISBN
978-0-387-79714-4 (Springer) . . . . . . 553--554
Michael De Villiers Book Review: \booktitleLeonhard Euler: a
man to be reckoned with, by Andreas
Heyne and Alice Heyne (illustrations by
Elena Pini). pp. 45. \pounds 14.50
(hardback). 2007. ISBN:
978-3-7643-8332-9. (Basel: Birkhäuser
Verlag) . . . . . . . . . . . . . . . . 555--555
Peter J. Giblin Book Review: \booktitleRecountings:
Conversations with MIT mathematicians,
ed. Joel Segel, pp. 441. \$49-00 (hbk).
2009. ISBN: 978-1-56881-449-0 (A. K.
Peters)} . . . . . . . . . . . . . . . . 555--557
Kiril Bankov Book Review: \booktitleCommunicating
mathematics in the digital era, by J. M.
Borwein, E. M. Rocha, and J. F.
Rodrigues. Pp. 325. \$49.00 (Hardback),
2008. ISBN 978-1-56881-410-0 (A. K.
Peters, Ltd.)} . . . . . . . . . . . . . 557--559
Paul Hudson Book Review: \booktitlePicturing the
uncertain world, by Howard Wainer. Pp.
244. \pounds 17.95 (hbk). 2009. ISBN:
978-0-691-13759-9 (Princeton University
Press) . . . . . . . . . . . . . . . . . 559--560
Mark Hunacek Book Review: \booktitleWhat is a number?
Mathematical concepts and their origins,
by Robert Tubbs. Pp. 305. \pounds 15-00.
2009. ISBN: 978-0-8018-9018-5 (Johns
Hopkins University Press) . . . . . . . 560--561
Kiril Bankov Book Review: \booktitleWhat is the
point? Motivation and the mathematics
crisis, by David Wells. Pp. 309. \pounds
10.00. 2008. ISBN 978-0-907944-11-9
(Rain Press) . . . . . . . . . . . . . . 561--562
Kiril Bankov Book Review: \booktitleMathematics
without fears, by Peter Sprent. pp. 453.
\pounds 14.59. 2009. ISBN
978-1-4092-5670-0 (Lulu) . . . . . . . . 562--563
Peter Shiu Book Review: \booktitleIntroduction to
metric & topological spaces (2nd edn.),
by Wilson A. Sutherland. Pp. 206 (hbk).
\pounds 45.00. 2009. ISBN:
978-0-19-956307-4 (Oxford University
Press) . . . . . . . . . . . . . . . . . 563--564
Peter Shiu Book Review: \booktitleElementary
functional analysis, by Barbara D.
MacCluer. Pp. 207. \pounds 29.99. 2009.
ISBN 978-0-387-85528-8 (Springer) . . . 564--564
Mark Hunacek Book Review: \booktitleMatrix
computations and semiseparable matrices
(Vol I: Linear Systems) Raf Vandebril,
Marc Van Barel and Nicola Mastronardi.
Pp. 575. \pounds 50. 2008. ISBN:
978-0-8018-8714-7 (Johns Hopkins
University Press) . . . . . . . . . . . 565--566
Nick Lord Book Review: \booktitleA course in
commutative Banach algebras, by E.
Kaniuth. pp. 353. 46.95 Euros. 2009.
ISBN 978-0-387-72475-1 (Springer) . . . 566--567
Bruce Roth Book Review: \booktitleCrosspacks & cross
hypersolids, by Patrick Taylor. Pp. 80.
\pounds 16.95. 2007. ISBN 0-9516701-8-2
(Nattygrafix, Ipswich) . . . . . . . . . 567--567
Graham H. Storr Book Review: \booktitleCrossing the
bridge, by Gerry Leversha. Pp. 180.
\pounds 11.00. 2008. ISBN
978-1-906001-06-3 (United Kingdom
Mathematics Trust) . . . . . . . . . . . 567--568
Paul Hudson Book Review: \booktitleFinite
mathematics, models and structure
(revised edition) by William J. Adams.
Pp. 619. \$23.99 (pbk). 2009. ISBN:
978-1-4363-3416-7 (Xlibis)} . . . . . . 568--569
John Haigh Book Review: \booktitleRisk and reward:
The science of casino blackjack, by N.
Richard Werthamer. Pp. 131. \pounds
44-99 (hbk). 2009. ISBN:
978-1-4419-0252-8 (Springer) . . . . . . 569--570
René L. Schilling Book Review: \booktitleA journey through
statistical physics. From foundations to
the quantum Hall effect: Selecta of Jürg
Fröhlich. Giovanni Felder, Gian Michele
Graf, Klaus Hepp (eds). Pp. 857. \pounds
126.00. 2009. ISBN: 13-978-1-4020-8886-5
(Springer) . . . . . . . . . . . . . . . 570--570
Dave Applebaum Book Review: \booktitleHilbert space
methods and quantum mechanics, by Werner
O. Amrein. Pp. 395. \$94.95 (hbk). 2009.
ISBN: 978-1-200-6681-4 (CRC Press)} . . 571--571
Gerry Leversha Book Review: \booktitleMusic, a
mathematical offering, by David J.
Benson. Pp. 411. \pounds 25.99. 2007.
ISBN 0-521-61999-8 (Cambridge University
Press) . . . . . . . . . . . . . . . . . 571--572
Michael Ward Book Review: \booktitleBefore sudoku:
the world of magic squares, by Seymour
S. Block and Santiago A. Tavares. Pp.
239. \pounds 7.99. 2009. ISBN:
978-0-19-536790-4 (Oxford University
Press) . . . . . . . . . . . . . . . . . 572--573
Tung Ken Lam and
Sue Pope Book Review: \booktitleMarvelous modular
origami, by Meenakshi Mukerji. Pp. 92.
\$14.95. 2007. ISBN: 978-1-56881-316-5
(A. K. Peters)} . . . . . . . . . . . . 573--573
Peter Shiu Book Review: \booktitlePythagoras'
revenge: a mathematical mystery, by
Arturo Sangalli. Pp. 183. \pounds 14.95.
2009. ISBN 978-0-691-04955-7 (Princeton
University Press) . . . . . . . . . . . 574--574
Peter Hall Book Review: \booktitleIt's a kind of
magic: mathematical magic tricks
explained, by David Crawford. pp. 258.
Members \pounds 19-99, Non-members
\pounds 23-99. 2009. ISBN: 0-906588-67-7
(The Mathematical Association) . . . . . 574--575
Anonymous MAG volume 94 issue 531 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 94 issue 531 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Anonymous Index to the \booktitleMathematical
Gazette . . . . . . . . . . . . . . . . i--ix
Anonymous MAG volume 95 issue 532--534 Cover and
Front matter . . . . . . . . . . . . . . f1--f1
John Sharp and
B. G. Nickel and
J. L. Hunt Anamorphoscopes another look at circle
inverting mirrors . . . . . . . . . . . 1--16
Thomas J. Osler Morphing Lord Brouncker's continued
fraction for $ \pi $ into the product of
Wallis . . . . . . . . . . . . . . . . . 17--22
Martin Griffiths and
Nick Lord The hook-length formula and generalised
Catalan numbers . . . . . . . . . . . . 23--30
Bojan Hvala Diophantine Steiner triples . . . . . . 31--39
Thomas J. Osler Euler's parallel oblique-angled
diameters . . . . . . . . . . . . . . . 40--48
A. J. Macfarlane The Morley tricorn a solid figure
constructed from the diagram for
Morley's theorem . . . . . . . . . . . . 49--51
Martin Griffiths The geometry of a stable game . . . . . 52--58
Roy Barbara 95.01 The rational distance problem . . 59--61
Michael D. Hirschhorn 95.02 Commensurable triangles . . . . . 61--63
Reginald Koo 95.03 Geometric enumeration of the
rationals between any two rational
numbers . . . . . . . . . . . . . . . . 63--66
C. W. Puritz 95.04 Make your own log table! . . . . . 66--72
W. J. A. Colman 95.05 Measuring the radius of the Earth 72--76
J. A. Scott 95.06 The harmonic series revisited . . 77--78
Juan Pla 95.07 Series for $ \pi \ln k $ and some
other mathematical constants . . . . . . 78--82
Michael D. Hirschhorn 95.08 Maximisation/minimisation without
calculus . . . . . . . . . . . . . . . . 83--85
Shailesh A. Shirali 95.09 A bootstrapping proof of the
AM--GM Inequality for three variables 86--87
Panakkal Mathew and
Imre Patyi 95.10 The fundamental theorem of
calculus implies that of algebra . . . . 88--89
Michael D. Hirschhorn 95.11 An interesting integral . . . . . 90--91
Robin Murphy 95.12 Accelerating the convergence of
some alternating series . . . . . . . . 91--96
Thomas Koshy and
Zhenguang Gao 95.13 Some divisibility properties of
Catalan numbers . . . . . . . . . . . . 96--102
Michael De Villiers 95.14 Equiangular cyclic and equilateral
circumscribed polygons . . . . . . . . . 102--107
Andrew K. Jobbings 95.15 Proofs by dissection of a
dodecagon . . . . . . . . . . . . . . . 107--110
C. J. Bradley 95.16 The generalisation of the
triplicate ratio circle . . . . . . . . 110--113
Chinmoy Kumar Ghosh 95.17 The golden ratio in conic sections 113--115
J. A. Scott 95.18 Normals to the Euler line . . . . 115--117
C. W. Groetsch 95.19 Spurt optimization . . . . . . . . 118--119
Alan F. Beardon 95.20 Integral inequalities in
probability theory . . . . . . . . . . . 119--123
Nick Lord The confusion between inverse and
reciprocal functions . . . . . . . . . . 124--125
Nick Lord Proof without words that $ 2 < e < 3 $ . . 125--126
Peter G. Brown Rays in a right triangle . . . . . . . . 126--127
Anonymous Feedback . . . . . . . . . . . . . . . . 128--132
Nick Lord Problem Corner . . . . . . . . . . . . . 133--141
Stan Dolan Student Problems . . . . . . . . . . . . 142--143
Peter Hall Book Review: \booktitleEssentials: KS3
mathematics coursebook, by Fiona Mapp.
Pp. 288. \pounds 13.00. 2009. ISBN:
978-1-844192-39-7 (Lonsdale) . . . . . . 144--144
Martin Griffiths Book Review: \booktitleStatistics GCSE
for AQA: (2nd edn.), by Jayne Kranat.
Pp. 330. \pounds 19.50. 2009. ISBN:
978-0-19-913430-4 (Oxford University
Press) . . . . . . . . . . . . . . . . . 144--145
Peter Hall Book Review: \booktitleStatistics: basic
principles and applications (2nd edn),
by William J. Adams, Irwin Kabus and
Mitchell P. Preiss. Pp. 731. \$23.99.
2009. ISBN: 978-1-4363-0180-0 (Xlibris)} 145--145
Peter Giblin Book Review: \booktitleDuel at dawn:
heroes, martyrs and the rise of modern
mathematics, by Amir Alexander. Pp. 307.
\pounds 21.95 2010. ISBN
978-0-674-04661-0 (Harvard University
Press) . . . . . . . . . . . . . . . . . 146--147
Paul Hudson Book Review: \booktitleMathematical
people: profiles and interviews (2nd
edn.), edited by Donald J. Albers and
Gerald L. Alexanderson. Pp. 385. \$59-00
(hardback). 2008. ISBN:
978-1-56881-340-0 (A. K. Peters)} . . . 147--149
Charles Eaton Book Review: \booktitleHistory of
mathematics: highways and byways, by Amy
Dahan-Dalmedico and Jeanne Peiffer. Pp.
330. \pounds 40.00 (hbk). 2010. ISBN:
978-0-888385-562-1 (Mathematical
Association of America) . . . . . . . . 149--150
P. N. Ruane Book Review: \booktitleThe mathematics
of the heavens and the earth: The early
history of trigonometry, by Glen van
Brummelen. Pp. 329. \pounds 23.95
(hardback). 2009. ISBN 978-0-691-12973-0
(Princeton University Press) . . . . . . 150--151
Michael Ward Book Review: \booktitleDecoding reality:
the universe as quantum information, by
Vlatko Vedral. Pp. 229. \pounds 16.99.
2010. ISBN 978-0-19-923769-2 (Oxford
University Press) . . . . . . . . . . . 151--152
S. C. Coutinho Book Review: \booktitleMathematics in
India, by Kim Plofker. Pp. 384. \$
39.50. 2009. ISBN: 978-0-691-12067-6
(Princeton University Press)} . . . . . 152--154
Gerry Leversha Book Review: \booktitleMathematics and
music, by David Wright. Pp. 161. \pounds
29.50. 2009. ISBN 978-0-8218-4873-9
(American Mathematical Society) . . . . 154--155
Nick Lord Book Review: \booktitleRiot at the calc.
exam and other Mathematically Bent
stories, by Colin Adams. Pp. 271. \$32.
2009. ISBN 978-0-8218-4817-3 (American
Mathematical Society)} . . . . . . . . . 155--156
Martin Griffiths Book Review: \booktitleThose fascinating
numbers, by Jean-Marie De Koninck. Pp.
426. \pounds 34.95. 2009. ISBN:
978-0-8218-4807-4 (American Mathematical
Society) . . . . . . . . . . . . . . . . 156--157
Peter Shiu Book Review: \booktitleThe finite simple
groups, by Robert A. Wilson. Pp. 298.
\pounds 53.45 (Hardback). 2009. ISBN:
978-1-84800-987-5. (Springer) . . . . . 157--159
Gerry Leversha Book Review: \booktitleSacred
mathematics, by Hidetoshi Fukagawa and
Tony Rothman. Pp. 348. \pounds 26.95.
2008. ISBN 978-0-691-12745-3 (Princeton
University Press). \booktitleTraditional
Japanese mathematics problems, by
Hidetoshi Fukagawa and John Rigby. Pp.
191. \$50. 2002. ISBN 981-04-2759-X (SCT
Publishing, Singapore)} . . . . . . . . 159--160
Peter Shiu Book Review: \booktitleFunctional
equations and inequalities with
applications, by PI. Kannappan. Pp. 810,
\pounds 117-00 (Hardback), 2009. ISBN:
978-0-387-89491-1. (Springer) . . . . . 160--162
Gerry Leversha Book Review: \booktitleGems of geometry,
by John Barnes. Pp. 311. \pounds 35.99
(hbk). 2009. ISBN 978-3-642-05091-6
(Springer) . . . . . . . . . . . . . . . 162--163
Nick Lord Book Review: \booktitleThe mathematical
colouring book: mathematics of colouring
and the colourful life of its creators,
by Alexander Soifer. Pp. 607. 42.95
euros. 2009. ISBN 978-0-387-74640-1
(Springer) . . . . . . . . . . . . . . . 163--165
Charlotte Anderson Book Review: \booktitleThe mathematical
mechanic, by Mark Levi. Pp. 186. \pounds
13.95 (hbk). 2009. ISBN
978-0-691-14020-9 (Princeton University
Press) . . . . . . . . . . . . . . . . . 165--166
P. MacGregor Book Review: \booktitleStability and
stabilization: an introduction, by
William J. Terrell. pp. 457. \pounds
40.95 (Hardback). 2009. ISBN:
978-0-691-13444-4 (Princeton University
Press) . . . . . . . . . . . . . . . . . 166--167
John Baylis Book Review: \booktitleThe Monty Hall
Problem --- the remarkable story of
math's most contentious brainteaser, by
Jason Rosenhouse. Pp. 194. \pounds
15.99. 2009. ISBN 978-0-195-36789-8
(Oxford University Press) . . . . . . . 167--169
Michael De Villiers Book Review: \booktitleA primer for
mathematics competitions, Alexander
Zawaira and Gavin Hitchcock. Pp. 338.
\pounds 50.00 (Hardback), \pounds 22-50
(Paperback). 2009. ISBN
978-0-19-953987-1; 978-0-19-953988-8
(Paperback). (Oxford University Press) 169--170
John Baylis Book Review: \booktitleMathematics as
problem solving (2nd edn), by Alexander
Soifer. Pp. 106. \pounds 35.99. 2009.
ISBN 978-0-387-74646-3 (Springer) . . . 171--171
Gerry Leversha Book Review: \booktitleSuperbrain: the
first twenty-five years, by Early
Diarmuid and MacHale. Des Pp. 230.
\pounds 13.00. 2009. ISBN:
978-1-906338-01-5 (HighPerception) . . . 171--172
Gerry Leversha Book Review: \booktitleProfessor
Stewart's hoard of mathematical
treasures, by Ian Stewart. Pp. 339.
\pounds 12.99. 2009. ISBN:
978-1-84668-292-6 (Basic Books) . . . . 172--173
Martin Griffiths Book Review: \booktitleA mathematical
medley: fifty easy pieces on
mathematics, by George G. Szpiro. Pp.
236. \pounds 26.95. 2010. ISBN:
978-0-8218-4928-6 (American Mathematical
Society) . . . . . . . . . . . . . . . . 173--174
Alan Sutcliffe Book Review: \booktitleA lifetime of
puzzles: A collection of puzzles in
honor of Martin Gardner's 90th birthday,
edited by Erik D. Demaine, Martin L.
Demaine, and Tom Rodgers. Pp. 349.
\pounds 38.95 (hbk). 2008. ISBN:
978-1-56881-245-8 (A. K. Peters).
Origami, Eleusis, and the Soma cube:
Martin Gardner's mathematical
diversions, (Volume 2 of The New Martin
Gardner Mathematical Library), by Martin
Gardner. Pp. 234. \pounds 8.99. 2008.
ISBN: 978-0-521-73524-7 (Cambridge
University Press) . . . . . . . . . . . 174--175
Anonymous MAG volume 95 issue 532 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 95 issue 532 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Philip C. Gager and
Mark B. Shackleton A snakes and ladders representation of
stock prices and returns . . . . . . . . 177--185
Tom M. Apostol and
Mamikon A. Mnatsakanian Sums of squares of integers in
arithmetic progression . . . . . . . . . 186--196
Shailesh A. Shirali A generalisation of the Arbelos Theorem
of Archimedes . . . . . . . . . . . . . 197--205
Peter Shiu Finding a missing digit . . . . . . . . 206--212
A. C. Paseau Family planning . . . . . . . . . . . . 213--217
M. J. Cooker Fast formulas for slowly convergent
alternating series . . . . . . . . . . . 218--226
Shailesh A. Shirali Triangles with one angle equal to 60
degrees . . . . . . . . . . . . . . . . 227--234
Juan Pla Some remarks about a formula of Charles
Dodgson . . . . . . . . . . . . . . . . 235--239
Lee Collins and
Thomas J. Osler Law of cosines generalised for any
polygon and any polyhedron . . . . . . . 240--243
G. J. O. Jameson Finding Carmichael numbers . . . . . . . 244--255
Martin Griffiths Is trigonometry the preserve of the
mathematical élite? . . . . . . . . . . . 256--261
Ognjen Milatovic 95.21 A property of odd terms of a
generalised Fibonacci sequence . . . . . 262--264
Alberto Zorzi 95.22 Benford's law and $ \pi $ . . . . 264--266
M. Chaves 95.23 Twin primes and a primality test
by indivisibility . . . . . . . . . . . 266--269
Stan Dolan 95.24 Fermat's method of ``descente
infinie'' . . . . . . . . . . . . . . . 269--271
Des Machale 95.25 Goldbach variations . . . . . . . 271--273
C. Johnson 95.26 Nice cubics . . . . . . . . . . . 273--279
Martin Griffiths 95.27 Symmetric rational expressions in
polynomial sequences . . . . . . . . . . 279--284
Bianca Edwards and
Jim Hartman 95.28 Powers of magic matrices . . . . . 284--292
Ondrej Such 95.29 The order of elements in $ {\rm
SL} (2, p) $ . . . . . . . . . . . . . . 292--300
Andrew M. Rockett and
Joseph P. Ruggerio 95.30 On Stråhle's guitar frets . . . . . 300--303
Robert M. Young 95.31 $ \int_0^\infty 1 / (1 + x^2) \, d
x = \pi / 2 $: A proof without
trigonometry . . . . . . . . . . . . . . 304--304
Robert M. Young 95.32 $ i n t_0^1 1 / (1 + x^2) \, d x =
\pi / 4 $: an elementary proof . . . . . 304--307
Robin V. W. Murphy 95.33 Integrating $ \int_0^\infty |
\sin^a(x) + \cos^b(x)| / x^p \, d x $ 307--311
Robert M. Young 95.34 On evaluating the probability
integral . . . . . . . . . . . . . . . . 311--313
Michael D. Hirschhorn 95.35 A surprising appearance of $ \zeta
(3) $ . . . . . . . . . . . . . . . . . 313--313
Nick Lord 95.36 Sequences of averages revisited 314--317
Nick Lord 95.37 An instructive application of the
inequality of means . . . . . . . . . . 317--319
Mitsuhiro Kumano 95.38 An extension of a certain
inequality in the 24th IMO . . . . . . . 320--321
Nick Lord 95.39 A UKMT Senior Mathematical
Challenge problem: frustration leads to
joy! . . . . . . . . . . . . . . . . . . 322--322
Michael D. Hirschhorn 95.40 Lord Brouncker's continued
fraction for $ \pi $ . . . . . . . . . . 322--326
Marcus Wright and
Thomas J. Osler 95.41 An interesting generalisation of
the half-angle formulas to complex
numbers . . . . . . . . . . . . . . . . 327--327
Terence Jackson 95.42 Irrational square roots of natural
numbers --- a geometrical approach . . . 327--330
Pratik Patel and
Robert Underwood 95.43 On convex quadrilaterals . . . . . 330--333
Nick Lord 95.44 Newton tackles an Olympiad problem 334--341
Mowaffaq Hajja 95.45 What do permutations of a given
cycle pattern generate? . . . . . . . . 341--342
Iliya Bluskov 95.46 Powers ending in $ 00 \ldots {}01
$ . . . . . . . . . . . . . . . . . . . 342--347
Hung-Ping Tsao 95.47 Sums of powers and Eulerian
numbers . . . . . . . . . . . . . . . . 347--349
Stuart Simons 95.48 Balls and walls --- how energy can
be lost in elastic collisions . . . . . 349--353
Nick Lord Reflection paths with restitution . . . 354--356
Nick Lord Binomial modes . . . . . . . . . . . . . 356--357
Colin Foster A comment on Schnell and Mendoza . . . . 357--357
K. Robin McLean Correspondence . . . . . . . . . . . . . 358--358
Anonymous Feedback . . . . . . . . . . . . . . . . 359--361
N. J. L. Problem Corner . . . . . . . . . . . . . 362--368
Stan Dolan Student Problems . . . . . . . . . . . . 369--371
Nick Lord Book Review: \booktitleMaking
mathematics come to life: a guide for
teachers and students, by O. A. Ivanov.
pp. 337. \pounds 55.95. 2009. ISBN
978-0-8218-4808-1 (American Mathematical
Society) . . . . . . . . . . . . . . . . 372--373
Peter Hall Book Review: \booktitleAssessment
methods in statistical education: an
international perspective, by Penelope
Bidgood, Neville Hunt and Flavia
Jolliffe (Editors). Pp. 286. \pounds
55.00. 2010. ISBN: 978-0-470-74532-8
(Wiley) . . . . . . . . . . . . . . . . 373--375
Graham Hoare Book Review: \booktitleThe Abel Prize
2003--2007: The first five years, by
Helge Holden and Ragui Piene (Editors).
Pp. 327. \pounds 58.99 (Hardback). 2010.
ISBN: 978-3-642-01372-0 (Springer) . . . 375--376
Paul Hudson Book Review: \booktitleMeta maths: the
quest for omega, by Gregory Chaitin. pp.
220. \pounds 9.99. 2007. ISBN:
978-1-84354-525-5 (Atlantic Books) . . . 377--379
Mary Fortune Book Review: \booktitleA mathematical
nature walk, by John Adam. pp. 249.
\pounds 16.95 (Hardback). 2009. ISBN:
978-0-691-12895-5 (Princeton University
Press) . . . . . . . . . . . . . . . . . 379--379
Gerry Leversha Book Review: \booktitleThe big
questions: mathematics, by Tony Crilly.
Pp. 208. \pounds 9.99. 2011. ISBN
978-1-84916-240-1 (Quercus) . . . . . . 379--380
Piotr Zarzycki Book Review: \booktitleIntroduction to
the practice of statistics, by David S.
Moore, George P. McCabe, Bruce A. Craig.
pp. 710. \pounds 49.99. 2009. ISBN
978-1-4292-1623-4 (W. H. Freeman and
Company) . . . . . . . . . . . . . . . . 380--381
Michael Ward Book Review: \booktitleFlatland: an
edition with notes and commentary, by
Edwin A. Abbott, William F. Lindgren and
Thomas F. Banchof. pp. 294. \pounds
9.99. 2010. ISBN 978-0-521-75994-6.
(Cambridge University Press) . . . . . . 381--382
Anne Haworth Book Review: \booktitleCows in the maze
and other mathematical explorations, by
Ian Stewart. pp. 287. \pounds 8.99.
2010. ISBN 978-0-19-956207-7 (Oxford
University Press) . . . . . . . . . . . 382--383
Nick Lord Book Review: \booktitleThe mathematics
of A-level statistics, by Owen Toller.
Pp. 56. \pounds 13.99. 2010. ISBN
978-0-906588-68-0 (The Mathematical
Association) . . . . . . . . . . . . . . 383--383
Anonymous MAG volume 95 issue 533 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 95 issue 533 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
David Acheson What's the Problem with Maths? . . . . . 386--394
Gerry Leversha Editorial . . . . . . . . . . . . . . . 394--396
Martin Griffiths A digit function with Thomae-like
properties . . . . . . . . . . . . . . . 397--403
Christopher J. Bradley Significant points on circles centre the
circumcentre . . . . . . . . . . . . . . 404--406
Li Zhou Irrationality proofs \`a la Hermite . . 407--413
Michael J. Cullinane Metric axioms and distance . . . . . . . 414--419
G. J. O. Jameson Finding pseudoprimes . . . . . . . . . . 420--432
Daniel Shiu and
Peter Shiu A lower bound for the prime counting
function . . . . . . . . . . . . . . . . 433--436
Stan Dolan A classification of Kaprekar constant 437--443
Sándor Dobos Cross ratio in use . . . . . . . . . . . 444--453
A. D. Keedwell Gaston Tarry and multimagic squares . . 454--468
Christopher J. Sangwin Limit-free derivatives . . . . . . . . . 469--482
Norman Routledge 95.49 Generalised Fibonacci Properties 483--486
N. Gauthier 95.50 Fractional-power identities for
Fibonacci and Lucas polynomials and
numbers . . . . . . . . . . . . . . . . 486--494
Juan Pla 95.51 On a multigrade congruence . . . . 494--496
W. J. A. Colman 95.52 A note on prime numbers . . . . . 497--501
Russell Euler and
Jawad Sadek 95.53 A formula for all $k$-gonal
numbers that are centred $k$-gonal . . . 501--505
Paul Loomis 95.54 Two results on sums of cubes . . . 506--510
Michael D. Hirschhorn 95.55 When is the sum of consecutive
squares a square? . . . . . . . . . . . 511--512
Mark B. Villarino 95.56 Burning mirrors on opening day . . 512--514
Michael D. Hirschhorn 95.57 A triangle-folding problem . . . . 514--517
J. A. Scott 95.58 On infinite series over the primes 517--518
J. A. Scott 95.59 Another series for the inverse
tangent . . . . . . . . . . . . . . . . 518--520
R. W. D. Nickalls 95.60 A new bound for polynomials when
all the roots are real . . . . . . . . . 520--526
Michael D. Hirschhorn 95.61 Tenth order algorithms for
calculating $ \sqrt (x), \sqrt [3]{3} $ 526--528
Robin Murphy 95.62 Numerical integration in a
spreadsheet . . . . . . . . . . . . . . 528--532
Thomas Koshy 95.63 Central binomial coefficients and
Catalan congruences . . . . . . . . . . 533--538
Andrew K. Jobbings 95.64 Two semicircles fill half a circle 538--540
Aidan Sudbury 95.65 Vectors and the nine-point circle 540--542
C.-S. Lin 95.66 The reciprocal volume of a Heron
tetrahedron . . . . . . . . . . . . . . 542--545
Stuart Simons 95.67 SHM on a rough surface . . . . . . 545--549
Jeremy D. King and
Nick Lord 95.68 The mechanics of sliding down
curves . . . . . . . . . . . . . . . . . 549--553
Stuart Simons Constant acceleration revisited . . . . 553--554
Osvaldo Marrero One equals zero: a specious argument . . 554--555
Nick Lord and
Alex Yan A difference in the behaviour of moments
of inertia and variance . . . . . . . . 556--557
Anonymous Feedback . . . . . . . . . . . . . . . . 557--559
Mark J. Cooker Correspondence . . . . . . . . . . . . . 560--561
John Mahony Correspondence . . . . . . . . . . . . . 561--561
Nick Lord Problem Corner . . . . . . . . . . . . . 562--567
Stan Dolan Student Problems . . . . . . . . . . . . 568--569
Peter Giblin Book Review: \booktitleFundamentals of
university mathematics, (3rd edn.),
Colin McGregor, Jonathan Nimmo and the
late Wilson Stothers. Pp. 551. \pounds
40 (pbk). 2010. ISBN 978-0-85709-223-6
(print), 978-0-85709-224-3 (online)
(Woodhead Publishing Paperback) . . . . 570--570
Dave Applebaum Book Review: \booktitleHarmonic analysis
of mean periodic functions on symmetric
spaces and the Heisenberg group, by
Valery V. Volchkov and Vitaly V.
Volchkov. Pp. 671 \$59. 99 (hbk). 2009.
ISBN 978-1-84882-532-1 (Springer
Monographs in Mathematics,
Springer-Verlag London Ltd.)} . . . . . 571--572
Martin Griffiths Book Review: \booktitleHow to guard an
art gallery: and other discrete
mathematical adventures, by T. S.
Michael. Pp. 257. \pounds 13.00. 2009.
ISBN: 978-0-8018-9299-8 (Johns Hopkins
University Press) . . . . . . . . . . . 572--572
Peter Giblin Book Review: \booktitleCinderella
(Version 2): Interactive geometry
package, by Ulrich Kortenkamp, EUR49.00
for single user licence, 2007. Available
for download at www.cinderella.de . . . 573--575
Anonymous Acknowledgements . . . . . . . . . . . . 575--575
Anonymous MAG volume 95 issue 534 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 95 issue 534 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Anonymous Index to the \booktitleMathematical
Gazette . . . . . . . . . . . . . . . . i--ix
Anonymous MAG volume 96 issue 535--537 Cover and
Front matter . . . . . . . . . . . . . . f1--f1
Richard Ellard and
Des MacHale Packing squares into rectangles . . . . 1--18
John Silvester Droz--Farny constructions . . . . . . . 19--38
Roger Eggleton and
Krzysztof Ostaszewski The 6666 Problem . . . . . . . . . . . . 39--48
R. W. D. Nickalls The quartic equation: alignment with an
equivalent tetrahedron . . . . . . . . . 49--55
Thomas Koshy Lobb's generalisation of Catalan's
parenthesisation problem revisited . . . 56--65
Stan Dolan Pell's equation and Fermat . . . . . . . 66--70
I. Grattan-Guinness Properties of inscribed and
circumscribed rectangles . . . . . . . . 71--77
Michael De Villiers Generalising a problem of Sylvester . . 78--81
N. Gauthier Closed forms for convolutions of Catalan
numbers . . . . . . . . . . . . . . . . 82--90
Des MacHale and
Christian van den Bosch 96.01 Generalising a result about
Pythagorean triples . . . . . . . . . . 91--96
K. S. Bhanu and
M. N. Deshpande 96.02 Dual Pythagorean triples . . . . . 96--99
Stan Dolan 96.03 Fermat's affirmative questions . . 99--102
A. F. Beardon 96.04 Pythagorean equations . . . . . . 102--103
I. Grattan-Guinness 96.05 On representing the square roots
of integers by straight lines . . . . . 104--106
J. Marshall Ash and
Yiren Tan 96.06 A rational number of the form $
a^a $ with $a$ irrational . . . . . . . 106--108
Colin Foster 96.07 Symmetrical cubics . . . . . . . . 109--112
Colin Foster 96.08 Orthogonal mappings . . . . . . . 112--115
Steven Donahue and
Thomas J. Osler 96.09 Euler's method of integration by
parts . . . . . . . . . . . . . . . . . 115--116
Robert M. Young 96.10 On an elementary proof of the
Leibniz formula for $ \pi $ . . . . . . 116--117
Martin Griffiths 96.11 Observations on some particular
power series . . . . . . . . . . . . . . 117--121
Martin Griffiths 96.12 The sum of a series: rational or
irrational? . . . . . . . . . . . . . . 121--124
Nick Lord 96.13 How Wallis's product approaches $
\pi $ . . . . . . . . . . . . . . . . . 124--127
Paul Levrie 96.14 Wallis's product formula for $ \pi
$: a symbolic approach . . . . . . . . . 127--129
Darrell Desbrow 96.15 Three infinite products . . . . . 130--131
Carl Barratt and
Ramesh Sharma 96.16 An inductive proof of the
condition for the AM--GM equality . . . 131--133
Michael D. Hirschhorn 96.17 Inequalities for Euler's constant 133--136
G. J. O. Jameson 96.18 Euler, Ioachimescu and the
trapezium rule . . . . . . . . . . . . . 136--142
Colin Foster 96.19 Taking a short cut through
Pascal's triangle . . . . . . . . . . . 142--145
Harlan J. Brothers 96.20 Pascal's triangle: The hidden
stor-$e$ . . . . . . . . . . . . . . . . 145--148
Nigel Derby 96.21 The MaxProduct Partition . . . . . 148--151
Martin Griffiths 96.22 Further thoughts on ordered
partitions . . . . . . . . . . . . . . . 152--153
Des MacHale and
Peter MacHale 96.23 Minimal Sudoku . . . . . . . . . . 153--156
Douglas Quadling 96.24 Genealogical algebra . . . . . . . 156--159
Andrew Percy 96.25 Going halfway with circular
boundaries . . . . . . . . . . . . . . . 159--160
J. A. Scott 96.26 The Exeter point revisited . . . . 160--161
Patricia R. Allaire and
Junmin Zhou and
Haishen Yao 96.25 Going halfway with circular
boundaries . . . . . . . . . . . . . . . 161--165
Andrew J. Simoson and
C. W. Groetsch 96.28 Spurtacular Fountains . . . . . . 166--168
King-Shun Leung Similar triangles and the Cosine Rule 169--172
Walter Milner A visual approach to Schnell and Mendoza 172--173
John Chick Correspondence . . . . . . . . . . . . . 174--174
Anonymous Feedback . . . . . . . . . . . . . . . . 174--176
Nick Lord Problem Corner . . . . . . . . . . . . . 177--182
Stan Dolan Student Problems . . . . . . . . . . . . 183--185
Gerry Leversha Book Review: \booktitleA transition to
advanced mathematics, by William
Johnston and Alex M. McAllister. Pp.
745. \$79.95 (Hardback). 2009. ISBN
978-0-19-531076-4 (Oxford University
Press)} . . . . . . . . . . . . . . . . 186--187
Peter Giblin Book Review: \booktitleThe mathematical
works of Leon Battista Alberti, Kim
Williams, Lionel March, Stephen R.
Wassell (eds.). Pp. 223. \pounds 69.
2010. ISBN 978-3-0346-0473-4 (Birkhäuser) 187--188
Charles Eaton Book Review: \booktitleThe symmetries of
things, by John Conway, Heidi Burgiel
and Chain Goodman-Strauss. Pp. 426.
\$75.00 (hbk). 2008. ISBN:
978-1-56881-220-5 (A. K. Peters)} . . . 187--190
Mary Fortune Book Review: \booktitlePattern theory:
tbe stochastic analysis of real-world
signals, by David Mumford and Agnes
Desolneux. Pp. 407. \$79-00 (hbk). 2010.
ISBN: 978-1-56881-579-4 (A. K. Peters)} 190--190
Anonymous MAG volume 96 issue 535 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 96 issue 535 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b4
Rasul A. Khan The probabilistic nature of Wallis's
formula . . . . . . . . . . . . . . . . 193--200
Juan Pla On a sequence of algebraic formulae of
Ramanujan . . . . . . . . . . . . . . . 201--206
A. F. Beardon What is the most symmetric
quadrilateral? . . . . . . . . . . . . . 207--212
Harlan J. Brothers Pascal's Prism . . . . . . . . . . . . . 213--220
Thomas J. Osler The missing fractions in Brouncker's
sequence of continued fractions for $
\pi $ . . . . . . . . . . . . . . . . . 221--225
David Benko Get rich slowly, almost surely . . . . . 226--235
Christopher Bradley Conics twinned with two special circles 236--242
Stuart Berry and
John Stubbs The mathematical modelling of population
change . . . . . . . . . . . . . . . . . 243--250
Shailesh A. Shirali Digging for roots using the Pascal spade 251--260
Shailesh A. Shiral 96.29 A party trick featuring the
triangular numbers . . . . . . . . . . . 261--263
Colin Foster 96.30 Quadratic doublets . . . . . . . . 264--266
J. R. Harris 96.31 Palindromic polynomials . . . . . 266--269
Tony Crilly 96.32 The `sums of squares' formula ---
a reprise . . . . . . . . . . . . . . . 269--271
Michel Daoud Yacoub and
Gustavo Fraidenraich 96.33 A solution to the quartic equation 271--275
Joshua A. Binder-Brantley 96.34 Determining the prime
factorisation of a matrix . . . . . . . 275--280
A. F. Beardon 96.35 Reflections on lattices . . . . . 280--283
R. V. W. Murphy 96.37 Evaluating $ I(\alpha) =
\int_0^\infty 1 / (1 + x^\alpha)^2 \, d
x $ using complex numbers . . . . . . . 287--289
Nick Lord 96.38 Evaluating integrals using polar
areas . . . . . . . . . . . . . . . . . 289--296
Nick Lord 96.39 Squares in triangles . . . . . . . 296--299
Douglas W. Mitchell 96.40 A property of hyperbolas and their
asymptotes . . . . . . . . . . . . . . . 299--301
David Gau 96.41 Triangle through an elliptical
looking-glass . . . . . . . . . . . . . 302--304
King-Shun Leung 96.42 Dividing a right-angled trapezium
into two similar quadrilaterals . . . . 304--309
Mowaffaq Hajja 96.44 Extremal properties of the
incentre and the excentres of a triangle 315--317
Philip W. Kuchel 96.45 Can you `bend' a truncated
truncated tetrahedron? . . . . . . . . . 317--323
Thomas Koshy 96.46 Some Catalan identities with
interesting consequence . . . . . . . . 323--328
Colin Foster 96.47 Squares within squares . . . . . . 328--331
Jonathan Weinstein 96.48 A result on zigzag permutations: a
combinatorial proof . . . . . . . . . . 331--333
Martin Griffiths 96.49 On the diagonals of a Stirling
number triangle . . . . . . . . . . . . 333--337
N. Gauthier and
Paul S. Bruckman 96.50 A note on a family of alternating
sums of products of binomial numbers . . 337--342
Wolfgang Slessenger A simple geometrical inequality . . . . 343--344
Nick Lord Quadrilaterals with area formula $ \sqrt
{a b c d} $ . . . . . . . . . . . . . . 345--347
Nick Lord Simultaneous construction of regular
$5$, $ 15$ and $ 60$-gons . . . . . . . 347--348
Nick Lord Shot putt with a height constraint . . . 348--350
Nick Lord Problem Corner . . . . . . . . . . . . . 351--356
Stan Dolan Student Problems . . . . . . . . . . . . 357--360
Geoff Tennant Book Review: \booktitleThinking
mathematically (Second Edition), by John
Mason, Leone Burton and Kaye Stacey. Pp.
248. \pounds 24.99. 2010. ISBN:
978-0-273-72891-7 (Pearson Education) 362--362
Graham H. Storr Book Review: \booktitleMathematics under
the microscope: notes on cognitive
aspects of mathematical practice, by
Alexandre V. Borovik. Pp. 317. \pounds
44.95 (hbk). 2010. ISBN:
978-0-8218-4761-9 (American Mathematical
Society) . . . . . . . . . . . . . . . . 362--363
Graham H. Storr Book Review: \booktitleGCSE revision
plus Edexcel mathematics for A* revision
guide, by Peter Sherran and Peter
Derych. Pp. 112. \pounds 5.99. 2010.
ISBN 978-1-84419-269-4 (Lonsdale). CSE
revision plus Edexcel mathematics higher
revision guide, by Peter Sherran. Pp.
112. \pounds 5.99. 2010. ISBN
978-1-84419-261-8 (Lonsdale) . . . . . . 363--364
Chris Munro Book Review: \booktitleAdvanced
engineering mathematics with MATLAB (3rd
edn.), by D. Duffy. Pp. 1079. \pounds
70-99. 2010. ISBN: 978-1-4398-1624-0
(CRC Press) . . . . . . . . . . . . . . 364--365
Peter Hall Book Review: \booktitleSuccess: AQA GCSE
mathematics higher revision guide, by
Fiona Mapp. Pp. 112. \pounds 4.99. 2010.
ISBN: 978-1-84419-286-1 (Letts).
Success: AQA GCSE mathematics higher
workbook, by Fiona Mapp. Pp. 96. \pounds
4.99, 2010. ISBN: 978-1-84419-287-8
(Letts) . . . . . . . . . . . . . . . . 365--366
Graham H. Storr Book Review: \booktitleEdexcel GCSE
mathematics higher workbook, by Peter
Sherran. Pp. 112. \pounds 5.99. 2010.
ISBN 978-1-84419-262-5 (Lonsdale) . . . 366--366
Ivor Grattan-Guinness Book Review: \booktitleMathematical
lives: protagonists of the twentieth
century, by Claudio Bartocci, Renato
Betti, Angelo Guerraggio and Roberto
Lucchetti (Editors). pp. 238. \pounds
53.99 (Hardback). 2011. ISBN:
978-3-642-13605-4 (Springer) . . . . . . 367--367
P. N. Ruane Book Review: \booktitleNewton's
philosophy of nature: selections from
his writings, by Isaac Newton (edited by
H. S. Thayer). Pp. 207. \$12-95. 2008.
ISBN 978-0-486-44593-9 (Dover)} . . . . 367--368
Peter Giblin Book Review: \booktitleGösta
Mittag-Leffler: a man of conviction, by
Arild Stubhaug. Translated by Tiina
Nunnally. Pp. 733. \pounds 53.99. 2010,
ISBN: 978-3-642-11671-1 (Springer) . . . 368--370
Gerry Leversha Book Review: \booktitleThe best writing
on mathematics 2010, edited by Mircea
Pitici. Pp. 407. \pounds 13.95. 2011.
ISBN 978-0-691-14841-0 (Princeton
University Press) . . . . . . . . . . . 370--371
Peter Shiu Book Review: \booktitleArithmetic of
quadratic forms, by Goro Shimura. Pp.
237, \pounds 64.99 (hbk), 2010. ISBN:
978-1-4419-1731-7 (Springer) . . . . . . 371--372
Mark Hunacek Book Review: \booktitleSymmetry,
representations and invariants, by Roe
Goodman and Nolan Wallach. Pp. 716.
\pounds 53.99 (Hardback). 2009. ISBN:
978-0-387-79851-6 (Springer) . . . . . . 372--373
P. MacGregor Book Review: \booktitleIntroduction to
inequalities, by C. J. Bradley. Pp. 210.
\pounds 11.00. 2010. ISBN:
978-1-906001-11-7 (United Kingdom
Mathematics Trust) . . . . . . . . . . . 374--374
S. C. Coutinho Book Review: \booktitleGeometric
mechanics and symmetry: from finite to
infinite dimensions, by D. D. Holm,
Tanya Schmah and Cristina Stoica. Pp.
384. U\$} 29.95 (Pbk). 2009. ISBN:
978-0-19-921291-0. (Oxford Texts in
Applied and Engineering Mathematics,
Oxford University Press)} . . . . . . . 374--376
Gerry Leversha Book Review: \booktitleGeometry
revealed, by Marcel Berger. Pp. 831.
\pounds 53.99. 2010. ISBN
978-3-540-70996-1 (Springer) . . . . . . 376--377
John Haigh Book Review: \booktitleProbability and
stochastics, by Erhan Çinlar. Pp. 557.
\pounds 53.00 (hbk). 2011. ISBN:
978-0-387-87858-4 (Springer) . . . . . . 377--378
Mark Hunacek Book Review: \booktitleMrs Perkins's
electric quilt: and other intriguing
stories of mathematical physics, by Paul
Nahin. Pp. 391. \pounds 20.95
(Hardback). 2009. ISBN:
978-0-961-13540-3 (Princeton University
Press) . . . . . . . . . . . . . . . . . 378--380
Graham Hoare Book Review: \booktitleRoads to
infinity: the mathematics of truth and
proof, by John Stillwell. Pp. 203.
\pounds 25.99 (Hardback). 2010. ISBN
978-1-56881-466-7 (A. K. Peters Ltd) . . 380--381
Martin Griffiths Book Review: \booktitleFamous puzzles of
great mathematicians, by M. Petkovi\'c.
Pp. 325. \pounds 25.95. 2009. ISBN:
978-0-8218-4814-2 (American Mathematical
Society) . . . . . . . . . . . . . . . . 381--382
Michael Ward Book Review: \booktitleFiguring it out:
entertaining encounters with everyday
math, by Nuno Crato. Pp. 227. \pounds
24.99. 2010. ISBN: 978-3-642-04832-6
(Springer) . . . . . . . . . . . . . . . 382--383
Jayaluxmi Naidoo Book Review: \booktitleOrigami
inspirations, by Meenakshi Mukerji. Pp.
120. \pounds 15.99. 2010. ISBN:
978-1-56881-584-8 (A. K. Peters) . . . . 383--383
Anonymous MAG volume 96 issue 536 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 96 issue 536 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Paul Andrews Learning from others Can PISA and TIMSS
really inform curriculum developments in
mathematics? . . . . . . . . . . . . . . 386--407
Daniel Shiu and
Peter Shiu A poor person's approximation to $ \pi $ 408--414
Roger W. Johnson `Toss Up' Strategies . . . . . . . . . . 415--419
Douglas Quadling A curious misattribution: the early
history of `Simson's line' . . . . . . . 420--427
A. H. G. S. van der Ven The Hardy distribution for golf hole
scores . . . . . . . . . . . . . . . . . 428--438
David Hopkins How many winners will there be? . . . . 439--450
Nick Lord Variations on a theme --- Euler and the
logsine integral . . . . . . . . . . . . 451--458
Tony Crilly How best should we vote? . . . . . . . . 459--465
Christopher Hollings I, Claudius and the cipher extraordinary 466--470
Ester Dalvit and
Domenico Luminati How to see a cube moving into its mirror
image . . . . . . . . . . . . . . . . . 471--479
Stan Dolan Fermat and the difference of two squares 480--491
Stan Dolan New points from old . . . . . . . . . . 492--498
Stephen Siklos Maclaurin's inequalities: reflections on
a STEP question . . . . . . . . . . . . 499--507
Paul Stephenson 96.51 Iterated dissections?
Approximations to $ \sqrt {2} $ in the
Indian Sulbasutras . . . . . . . . . . . 508--512
Martin Griffiths 96.52 Some different approaches to
summing a particular series . . . . . . 512--515
Thomas J. Osler 96.53 Partial sums of series that cannot
be an integer . . . . . . . . . . . . . 515--519
Paul Glaister 96.54 Further examples on sliding down
curves . . . . . . . . . . . . . . . . . 519--523
Denis Ibadula and
Dirk Segers 96.55 Convex proofs of some inequalities 523--526
Andrew Holman 96.56 How to drive too fast and not save
time . . . . . . . . . . . . . . . . . . 526--528
Anthony C. Robin 96.57 Stability of flotation, a look at
the metacentre . . . . . . . . . . . . . 529--536
Stuart Simons 96.58 Hauling a sledge and related
matters . . . . . . . . . . . . . . . . 536--541
Anonymous Acknowledgements . . . . . . . . . . . . 541--541
Des MacHale Mathematics and Humour . . . . . . . . . 542--543
Martin Griffiths Yet another coin-tossing scenario . . . 543--546
Peter Shiu Partitioning triangles . . . . . . . . . 546--550
Douglas Quadling Edwin Kerr (1926--2012) . . . . . . . . 551--552
Anonymous Feedback . . . . . . . . . . . . . . . . 553--559
Nick Lord Problem Corner . . . . . . . . . . . . . 560--566
Stan Dolan Student Problems . . . . . . . . . . . . 567--569
Gábor Megyesi Book Review: \booktitleDeformation
theory, by Robin Hartshorne. Pp. 234.
\pounds 58.80 (hbk). 2010. ISBN:
978-1-4419-1595-5 (Springer) . . . . . . 570--570
Gerry Leversha Book Review: \booktitleSix gems of
geometry, by Thomas Reale. Pp. 128.
\$14.99 (hbk). 2010. ISBN:
978-1-935638-02-5 (Perfectly Scientific
Press)} . . . . . . . . . . . . . . . . 570--572
Anne Haworth Book Review: \booktitleStreet-fighting
mathematics: the art of educated
guessing and opportunistic problem
solving, by Sanjoy Mahajan. Pp. 134.
\pounds 18.95. 2010. ISBN:
978-0-262-51429-3. (MIT Press) . . . . . 572--573
John Baylis Book Review: \booktitleProblem solving
--- the creative side of mathematics, by
Derek Holton. Pp. 211. \pounds 11.99
(members), \pounds 14.99 (non-members).
2010. ISBN: 978-0-906588-71-0 (The
Mathematical Association) . . . . . . . 573--574
Anonymous MAG volume 96 issue 537 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 96 issue 537 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b4
Anonymous Index to the \booktitleMathematical
Gazette . . . . . . . . . . . . . . . . iii--xi
Anonymous MAG volume 97 issue 538--540 Cover and
Front matter . . . . . . . . . . . . . . f1--f1
A. S. Di Domenico Integer sequences that behave as
Fibonacci--Lucas pairs . . . . . . . . . 1--7
Anthony Sudbery Dürer's magic tesseract . . . . . . . . . 8--12
David Hopkins Slide rules, nomograms and additive
functions . . . . . . . . . . . . . . . 13--26
Thomas Koshy Pell Walks . . . . . . . . . . . . . . . 27--35
B. Sury Composition of polynomials . . . . . . . 36--42
Christoph Kirfel A generalisation of Archimedes' method 43--52
Gerry Leversha A direct derivation of the Catalan
formula . . . . . . . . . . . . . . . . 53--60
Andrew Fabian and
Hieu D. Nguyen Paradoxical Euler: Integrating by
Differentiating . . . . . . . . . . . . 61--74
I. Grattan-Guinness On proving certain optimisation theorems
in plane geometry . . . . . . . . . . . 75--80
Barry Lewis How many dead ends in a derangement? . . 81--94
A. F. Beardon Frieze groups, cylinders, and quotient
groups . . . . . . . . . . . . . . . . . 95--100
Christopher Ormell Mathematics, a third way . . . . . . . . 101--106
Drago Bajc 97.01 Power solutions of some
Diophantine equations . . . . . . . . . 107--110
Peter Shiu 97.02 Solutions to $ \phi (m) = k! $ and
$ \sigma (n) = k! $ . . . . . . . . . . 110--115
Ragha Vendra G. Kulkarni 97.03 Insert a root to crack the cubic 115--120
Ragha Vendra G. Kulkarni 97.04 The solution of quintic equations 120--122
Munir Mahmood and
Ibtihal Mahmood 97.05 Two proofs without words . . . . . 123--124
Erik Talvila 97.06 Trigonometry of The Gold-Bug . . . 124--127
Graham J. O. Jameson and
Timothy P. Jameson 97.07 Four methods for a trigonometric
integral . . . . . . . . . . . . . . . . 127--131
Cory Wright and
Thomas J. Osler 97.08 Interesting bilateral series
generalising a result of Euler . . . . . 131--133
Thomas J. Osler and
Steven Donahue 97.09 The devil's series --- Did it fool
Euler? . . . . . . . . . . . . . . . . . 133--137
G. J. O. Jameson 97.10 Continuous functions that are not
differentiable anywhere . . . . . . . . 137--143
Roy Barbara 97.11 The rational distance problem for
polygons . . . . . . . . . . . . . . . . 144--149
Jim Farmer 97.12 Using Taylor's formula to compare
compound and simple interest . . . . . . 150--153
Shailesh A. Shirali 97.13 A circular locus . . . . . . . . . 153--157
Hiroshi Okumura 97.14 The area of a generalised arbelos 157--160
Norman Routledge 97.15 Iterating to find sines and
cosines . . . . . . . . . . . . . . . . 160--162
Carl Mungan and
Trevor Lipscombe 97.16 Probability analysis for rolls of
a square cuboidal die . . . . . . . . . 163--166
Trevor Lipscombe Mental mathematics for multiples of $
\pi $ . . . . . . . . . . . . . . . . . 167--169
Nick Lord Why the path of quickest descent is not
a straight line . . . . . . . . . . . . 169--171
Chris Little Fortuitous functions . . . . . . . . . . 172--172
Anonymous Feedback . . . . . . . . . . . . . . . . 172--177
Nick Lord Problem Corner . . . . . . . . . . . . . 178--183
Stan Dolan Student Problems . . . . . . . . . . . . 184--186
Graham Hoare Book Review: \booktitleThe mathematical
writings of Évariste Galois, by Peter M.
Neumann. Pp. 421. \pounds 74.50 (hbk.)
2011. ISBN: 978-3-03719-104-0 (European
Mathematical Society) . . . . . . . . . 187--188
Gerry Leversha Book Review: \booktitleMathematics in
Victorian Britain, by Raymond Flood,
Adrian Rice and Robin Wilson (eds.). Pp.
466. \pounds 29.99 (hbk). 2011. ISBN:
978-0-19-960139-4 (Oxford University
Press) . . . . . . . . . . . . . . . . . 188--190
Martin Griffiths Book Review: \booktitleFisber, Neyman,
and tbe creation of classical
statistics, by Erich Lehmann. Pp. 115.
\pounds 24.99. 2011. ISBN:
978-1-4419-9499-8 (Springer) . . . . . . 190--191
Peter MacGregor Book Review: \booktitleOrigami design
secrets: mathematical methods for an
ancient art, by Robert Lang. Pp. 758.
\pounds 38.99. 2011. ISBN:
978-1-56881-436-0 (CRC Press) . . . . . 191--191
Anonymous MAG volume 97 issue 538 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 97 issue 538 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
J. R. Nurcombe Alteration in the sum of alternating
series by simple rearrangement . . . . . 193--197
W. J. A. Colman Reflections on the Woolwich Ferry . . . 198--204
Graham J. O. Jameson and
Timothy P. Jameson Some remarkable integrals derived from a
simple algebraic identity . . . . . . . 205--209
Andrew Jobbings Folding a triangle . . . . . . . . . . . 210--217
Subhranil De Revisiting the sliding ladder . . . . . 218--223
Des MacHale and
Peter MacHale Relations on Sets . . . . . . . . . . . 224--233
Martin Griffiths From golden-ratio equalities to
Fibonacci and Lucas identities . . . . . 234--241
Robert Granger Could, or should, the ancient Greeks
have discovered the Lucas--Lehmer test? 242--255
Peter Shiu The gaps between sums of two squares . . 256--262
J. R. Collis 97.17 On products of multiplicative
functions . . . . . . . . . . . . . . . 263--264
Des MacHale and
Joseph Manning 97.18 Variations on twin primes . . . . 265--268
Raghavendra G. Kulkarni 97.19 Shifting the origin to solve
quartic equations . . . . . . . . . . . 268--270
Thomas Dence 97.20 Evaluating a common improper
integral . . . . . . . . . . . . . . . . 270--272
Man Keung Siu 97.21 Some more on Estermann and
Pythagoras . . . . . . . . . . . . . . . 272--273
Rodney Nillsen 97.22 A proof that the series $ \sum_{n
= 1}^\infty 1 / n^p $ is convergent for
$ p > 1 $ . . . . . . . . . . . . . . . . 273--274
Mark B. Villarino and
Daniel Campos Salas and
Javier Carvajal Rojas 91.23 On the monotonocity of the
correction term in Ramanujan's factorial
approximation . . . . . . . . . . . . . 274--275
Michael D. Hirschhorn 97.24 A constant in a formula of
Ramanujan . . . . . . . . . . . . . . . 276--277
Peter R. Mercer and
Allan A. Sesay 97.25 Error terms for Jensen's and
Levinson's Inequalities . . . . . . . . 277--280
Rasul A. Khan 97.26 The cosine rule in three
dimensions and de Gua's theorem . . . . 281--284
T. N. L. Patterson 97.27 Two rectangles and an intersection 284--290
Katharine Nunes 97.28 Inscribed circles and spheres . . 290--294
Nick Lord 97.29 A family of Heron-type formulae
for the triangle . . . . . . . . . . . . 294--297
Andrew Jobbings 97.30 Shapes with a skew square as
boundary . . . . . . . . . . . . . . . . 297--301
Paul Glaister 97.31 Tangents and coincident normals to
a parabola . . . . . . . . . . . . . . . 301--303
J. A. Scott 97.32 An areal view of the Morley
triangle . . . . . . . . . . . . . . . . 304--306
Stuart Simons 97.33 An extremum problem . . . . . . . 306--308
Nick Lord 97.34 An area inequality for
subtriangles of a quadrilateral . . . . 308--311
A. Donald Keedwell 97.35 A Problem of sociable dining . . . 311--315
Douglas Quadling 97.36 The isles to the road . . . . . . 315--317
Anthony C. Robin 97.37 End moves in a dice game . . . . . 318--324
Norman Routledge 97.38 The 6666 problem and state
diagrams . . . . . . . . . . . . . . . . 324--328
Samuel G. Moreno and
Esther M. García-Caballero Entry $ 1.414 \ldots $ in Ramanujan's
Notebooks: $ \sqrt {2} $ is irrational 329--329
Andrew Holman How to pull an object effectively . . . 330--333
Munir Mahwood Proof without words: a characterisation
of the difference of two squares . . . . 333--334
Robert M. Young Another quick proof that $ e < 3 $ . . . 333--334
Peter James Teaching Quadratic Functions . . . . . . 335--335
Nick Lord Binomial averages: an erratum . . . . . 336--336
Anonymous Feedback . . . . . . . . . . . . . . . . 337--340
Nick Lord Problem Corner . . . . . . . . . . . . . 341--349
Stan Dolan Student Problems . . . . . . . . . . . . 350--352
Gerry Leversha Book Review: \booktitleMath for the
frightened, by Colin Pask. Pp. 380.
\pounds 16.99. 2011. ISBN:
978-1-61614-421-0 (Prometheus Books) . . 353--354
Peter Hall Book Review: \booktitleCollins New Maths
Frameworking Level 6, booster workbook
(no author specified). Pp. 116. \pounds
5.99. 2011. ISBN: 978-0-00-743808-2
(Collins) . . . . . . . . . . . . . . . 354--355
P. MacGregor Book Review: \booktitleFundamental maths
for engineering and science, by Mark
Breach. Pp. 380. \pounds 25.99. 2011.
ISBN: 978-0-230-25208-0 (Palgrave
Macmillan) . . . . . . . . . . . . . . . 355--355
Martin Griffiths Book Review: \booktitleFundamental maths
for engineering and science, by Mark
Breach. Pp. 380. \pounds 25.99. 2011.
ISBN: 978-0-230-25208-0 (Palgrave
Macmillan) . . . . . . . . . . . . . . . 355--356
Owen Toller Book Review: \booktitleProgress to
advanced mathematics, by Mary Teresa
Fyfe, Andrew Jobbings, Kitty Kilday and
Mary Read Pp. 168 \pounds 9.00 plus
delivery 2011 ISBN: 978-0-9555477-3-7
(Arbelos) . . . . . . . . . . . . . . . 356--357
Charlotte Anderson Book Review: \booktitleThe quantum story
a history in 40 moments by Jim Baggott
Pp. 469 \pounds 16.99 (hbk). 2011. ISBN:
978-0-19-956684-6 (Oxford University
Press) . . . . . . . . . . . . . . . . . 357--358
Paul Hudson Book Review: \booktitleHow to read
historical mathematics, by Benjamin
Wardhaugh, Pp. 116. \pounds 15.95.(hbk)
2010. ISBN: 978-0-691-14014-8 (Princeton
University Press) . . . . . . . . . . . 358--359
Gerry Leversha Book Review: \booktitleHidden harmonies:
the lives and times of the Pythagorean
theorem, Robert and Ellen Kaplan. Pp.
280. \pounds 25. 2011. ISBN
978-1-59691-522-0 (Bloomsbury Press) . . 360--361
Gerry Leversha Book Review: \booktitleThe great
mathematicians, by Raymond Flood and
Robin Wilson. Pp. 208. \pounds 9.99.
2011 ISBN: 987-1-84837-902-2 (Arcturus) 361--362
P. N. Ruane Book Review: \booktitleAncient Indian
leaps into mathematics, B. S. Yadav and
Man Mohan (eds). Pp. 217. \pounds 66.99
(Hardback). 2011 ISBN: 978-0-8176-4694-3
(Birkhäuser) . . . . . . . . . . . . . . 362--363
Peter Giblin Book Review: \booktitleRemembering Sofya
Kovalevskaya, by Michéle Audin. Pp. 284.
\pounds 35.99. 2011 ISBN:
978-0-85729-928-4 (Springer-Verlag) . . 363--364
Mark Hunacek Book Review: \booktitleLoving + hating
mathematics: challenging the myths of
mathematical life, by Reuben Hersh and
Vera John-Steiner. Pp. 416. \$29.95
(Hardback). 2011 ISBN: 978-0-691-14247-0
(Princeton University Press)} . . . . . 364--367
Michael Ward Book Review: \booktitleMathematics is
precise, period, vs. mathematics is
precise, strings attached, by William J.
Adams. Pp. 492. \pounds 23.00. 2010
ISBN: 978-1-4363-3419-8 (Xlibris
Corporation) . . . . . . . . . . . . . . 367--367
Tony Crilly Book Review: \booktitleNumbers: a very
short introduction, by Peter Higgins.
Pp. 132 \pounds 7.99. 2011 ISBN:
978-0-19-958405-5 (Oxford University
Press) . . . . . . . . . . . . . . . . . 367--368
Nick Lord Book Review: \booktitleA course in
commutative algebra, by Gregor Kemper.
Pp. 246. \pounds 44.99. 2011. ISBN:
978-3-642-03544-9 (Springer) . . . . . . 369--369
Mark Hunacek Book Review: \booktitleDifferential
geometry of curves and surfaces, by
Thomas Banchoff and Stephen Lovett. Pp.
331. \$49.00 (Hardback). 2010. ISBN:
978-1-56881-456-8 (A. K. Peters)} . . . 370--371
Charles Eaton Book Review: \booktitleCellular automata
and groups, by Tullio
Ceccherini-Silberstein and Michel
Coornaert. Pp. 439. \pounds 81.00 (hbk).
2010 ISBN: 978-3-642-14033-4 (Springer) 371--372
Peter MacGregor Book Review: \booktitleDifferential
geometry of manifolds, by Stephen
Lovett. Pp. 421. \pounds 53.99 (hbk).
2010. ISBN 978-1-56881-457-5 (A. K.
Peters) . . . . . . . . . . . . . . . . 372--373
Peter Giblin Book Review: \booktitleDifferential
geometry: bundles, connections, metrics
and curvature, by Clifford Henry Taubes.
Pp. 298. \pounds 27.50. 2011. ISBN
978-0-19-960587-3 (Oxford Graduate Texts
in Mathematics No. 23, Oxford University
Press) . . . . . . . . . . . . . . . . . 373--373
Martin Griffiths Book Review: \booktitleThe colours of
infinity: the beauty and power of
fractals, by Nigel Lesmoir-Gordon (ed.).
Pp. 207 \pounds 29.95 (Hardback). 2010.
ISBN: 978-1-84996-485-2 (Springer) . . . 373--374
Peter Shiu Book Review: \booktitleMathematical
inequalities: a perspective, by Pietro
Cerone and Sever S. Dragomir. Pp. 391.
\pounds 76.99 (hbk). 2011. ISBN:
978-1-4398-4896-8 (CRC Press) . . . . . 374--375
René L. Schilling Book Review: \booktitleThe Oxford
handbook of random matrix theory, Gernot
Akemann, Jinho Baik, Philippe Di
Francesco (eds) Pp. 919. \pounds 110.
2011. ISBN: 978-0-19-957400-1 (Oxford
University Press) . . . . . . . . . . . 375--376
Ken Zetie Book Review: \booktitleCosmic numbers:
the numbers that define our universe, by
James D. Stein. Pp. 272. \pounds 17.99.
2011. ISBN 978-0-465-02198-7 (Basic
Books) . . . . . . . . . . . . . . . . . 376--378
Martin Griffiths Book Review: \booktitlePerfect rigour: a
genius and the mathematical breakthrough
of the century, by Masha Gessen Pp. 242
\pounds 14.99 (Hardback). 2011. ISBN:
978-1-84831-238-8 (Icon Books) . . . . . 378--378
Michael Ward Book Review: \booktitleTrain your brain:
a year's worth of puzzles, by George
Grätzer. Pp. 235. \pounds 18.99. 2011.
ISBN: 978-1-56881-710-1 (CRC Press) . . 380--380
Michael Ward Book Review: \booktitleTrain your brain:
a year's worth of puzzles, by George
Grätzer. Pp. 235. \pounds 18.99. 2011.
ISBN: 978-1-56881-710-1 (CRC Press) . . 380--380
P. G. MacGregor Book Review: \booktitleOrieami 5, by
Patsy Wang-Iverson, Robert J. Lang and
Mark Yim (eds) Pp. 646. \pounds 43.99.
2011. ISBN: 978-1-56881-714-9 (CRC
Press) . . . . . . . . . . . . . . . . . 381--382
Mary Fortune Book Review: \booktitleCrafting by
concepts, by Sarah-Marie Belcastro and
Carolyn Yackel. Pp. 248. \pounds 25.99
(hbk) 2011 ISBN: 978-1-56881-435-3 (A.
K. Peters) . . . . . . . . . . . . . . . 382--383
Anonymous MAG volume 97 issue 539 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 97 issue 539 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Marcus du Sautoy Teaching the Shakespeare of Mathematics 386--397
Mike Price and
Mary Walmsley R. L. Goodstein and the Mathematical
Association . . . . . . . . . . . . . . 398--408
Graham Hoare R. L. Goodstein and mathematical logic 409--412
John D. Mahony Gauging the earth . . . . . . . . . . . 413--420
G. C. Shephard Regular Polyhedral Clones . . . . . . . 421--429
Samuel G. Moreno and
Esther M. García-Caballero $ \Gamma^2 (1 / 2) $ is more than just $
\pi $ . . . . . . . . . . . . . . . . . 430--434
Isaac Sofair Derangement revisited . . . . . . . . . 435--440
Michael De Villiers 3D Generalisations of Viviani's theorem 441--445
Aristides V. Doumas An alternative approach to a problem by
A. de Moivre . . . . . . . . . . . . . . 446--454
John Melville A simple series representation for
Apéry's constant . . . . . . . . . . . . 455--460
Jawad Sadek and
Russell Euler Divisibility properties for Fibonacci
and related numbers . . . . . . . . . . 461--464
Li Zhou Fun with Sign . . . . . . . . . . . . . 465--473
Russell A. Gordon Splitting a triangle . . . . . . . . . . 474--493
John Conway and
Alex Ryba 97.39 Fibonometry . . . . . . . . . . . 494--495
Des MacHale 97.40 Infinitely many proofs that there
are infinitely many primes . . . . . . . 495--498
Stan Dolan 97.41 The equation $ p y^2 = x^4 + x $ 498--501
J. E. T. Trainin 97.42 The Bombelli approach to solving
cubic equations . . . . . . . . . . . . 501--504
G. J. O. Jameson and
Nick Lord 97.43 Evaluation of $ \sum_{n =
1}^\infty 1 / n^2 $ by a double integral 504--505
Tim Jameson 97.44 Another proof that $ \zeta (2) =
\pi^2 / 6 $ via double integration . . . 506--507
Imre Patyi 97.45 On Euler's Basel problem . . . . . 508--510
A. McD. Mercer 97.46 A new mean value theorem for
integrals . . . . . . . . . . . . . . . 510--512
Hiroshi Okumura 97.47 Archimedean twin circles in the
arbelos . . . . . . . . . . . . . . . . 512--512
J. A. Scott 97.48 The Kiepert hyperbola revisited 513--515
K. C. Chan and
C. T. Lenard and
T. M. Mills 97.49 On Markov chains . . . . . . . . . 515--520
T. Nigel Lucas 97.50 Further derivatives of
trigonometric functions using mechanics 520--523
Randall Baumback A tale of two triangles: a collaboration
between teacher and students . . . . . . 524--532
Martin Griffiths and
Surajit Rajagopal Conjecturing a limit . . . . . . . . . . 532--535
Nick Lord Two surprising maximisation problems . . 535--537
Anonymous Feedback . . . . . . . . . . . . . . . . 538--543
Nick Lord Problem Corner . . . . . . . . . . . . . 544--550
Stan Dolan Student Problems . . . . . . . . . . . . 551--553
Charlotte Anderson Book Review: \booktitleMathematical
expeditions: exploring word problems
across the ages, by Frank Swetz. pp.
192. \pounds 15.50. 2012. ISBN:
978-1-4214-0438-7 (Johns Hopkins
University Press) . . . . . . . . . . . 554--555
Gerry Leversha Book Review: \booktitleA wealth of
numbers, by Benjamin Wardhaugh. Pp. 370
\pounds 30.95. 2012. ISBN:
978-0-691-14775-8 (Princeton University
Press) . . . . . . . . . . . . . . . . . 555--556
Gerry Leversha Book Review: \booktitleThe crossing of
heaven: memoirs of a mathematician, by
Karl Gustafson. Pp. 176. \$59.95. 2012.
ISBN 978-3-642-22557-4 (Springer)} . . . 557--557
John Haigh Book Review: \booktitleGolf by the
numbers, by Roland Minton. Pp. 291
\pounds 18.00 (hbk). 2012. ISBN:
978-1-4214-0315-1 (Johns Hopkins
University Press) . . . . . . . . . . . 557--558
Stephen Rout Book Review: \booktitleFuelling
innovation and discovery. The
mathematical sciences in the 21st
century, by The National Research
Council of the National Academies. Pp.
57. \pounds 13.99. 2012. ISBN
978-0-309-25473-1 (The National
Academies Press.) . . . . . . . . . . . 558--559
Paul Hudson Book Review: \booktitleNumbers rule: the
vexing mathematics of democracy from
Plato to the present, by George G.
Szpiro. Pp. 226 \pounds 18.95
(Hardback). 2010. ISBN: 9780-691-13994-4
(Princeton University Press) . . . . . . 559--560
Gerry Leversha Book Review: \booktitleMaths on trial:
how numbers get used and abused, by
Leila Schneps and Coralie Colmez. Pp.
236. \pounds 17.99. 2013. ISBN:
978-0-465-03292-1 (Basic Books) . . . . 560--562
Gerry Leversha Book Review: \booktitleMath goes to the
movies, by Burkhard Polster and Marty
Ross Pp. 286. \pounds 18.00. 2012. ISBN:
978-1-4214-0484-4 (Johns Hopkins
University Press) . . . . . . . . . . . 562--563
Charlotte Anderson Book Review: \booktitleThe ballet of the
planets: on the mathematical elegance of
planetary motion, by Donald C. Benson.
Pp. 162. \$35.00 (Hardback). 2012. ISBN:
978-0-19-989100-9 (Oxford University
Press)} . . . . . . . . . . . . . . . . 563--565
Kiril Bankov Book Review: \booktitleMeasurement, by
Paul Lockhart. Pp. 398. \pounds 20.00.
2012. ISBN: 978-0-674-05755-5 (Harvard
University Press) . . . . . . . . . . . 565--566
Ian Anderson Book Review: \booktitleMathematical
excursions to the world's great
buildings, by Alexander J. Hahn. Pp.
318. \pounds 34.95.(Hardback). 2012.
ISBN: 978-0-691-14520-4 (Princeton
University Press) . . . . . . . . . . . 566--567
Mark Hunacek Book Review: \booktitleA prime puzzle,
by Martin Griffiths. Pp. 217. \pounds
12.00. 2012. ISBN: 978-1-906001-16-2
(The United Kingdom Mathematics Trust) 568--569
Matin Griffiths Book Review: \booktitleThe irrationals:
A story of the numbers you can't count
on, by Julian Havil. Pp. 298. \pounds
19.95 (Hardback). 2012. ISBN:
978-0-691-14342-2 (Princeton University
Press) . . . . . . . . . . . . . . . . . 569--570
Mark Hunacek Book Review: \booktitleA first course in
applied mathematics, by Jorge Rebaza.
Pp. 439. \pounds 76.95. (hbk) 2012.
ISBN: 978-1-118-22962-0 (Wiley) . . . . 570--571
Peter MacGregor Book Review: \booktitleLinear algebra
and probability for computer science
applications, by Ernest Davis. Pp. 413.
2012. ISBN 978-1-4665-0155-3 (CRC press) 572--572
S. C. Coutinho Book Review: \booktitleDynamics of
biological systems, by Michael Small.
Pp. 262. (2012). \pounds 49.99. ISBN
978-1-4398-5336-8 (Hardback),
(Mathematical and Computational Biology
Series, Chapman & Hall/CRC) . . . . . . . 572--574
David Bevan Book Review: \booktitleTaking Sudoku
seriously: The math behind the world's
most popular pencil puzzle, by Jason
Rosenhouse and Laura Taalman. pp. 214.
\pounds 13.99.(hbk) 2011. ISBN:
978-0-19-975656-8 (Oxford University
Press) . . . . . . . . . . . . . . . . . 574--575
Anonymous MAG volume 97 issue 540 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 97 issue 540 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
John Mason Uniqueness of patterns generated by
repetition . . . . . . . . . . . . . . . 1--7
Mark Hennings and
Jon Ingram Sliding in rough convex bowls . . . . . 8--23
Michael Fox Quadritangent spheres . . . . . . . . . 24--39
Owen Toller Misunderstandings in A-level statistics 40--50
Thomas Dence Holmes + Moriarty = Mathematics . . . . 51--57
G. J. O. Jameson Series involving $ \zeta (n) $ . . . . . 58--66
Takeshi Hokuto and
Mitsuhiro Kumano Which is bigger? An intriguing `double
alternation' . . . . . . . . . . . . . . 67--72
Subhranil De On static equilibrium of a hemispheroid 73--78
Fengming Dong and
Dongsheng Zhao and
Weng Kin Ho On the largest outscribed equilateral
triangle . . . . . . . . . . . . . . . . 79--84
G. J. O. Jameson An approximation to the
arithmetic--geometric mean . . . . . . . 85--95
G. J. O. Jameson Some inequalities for $ (a + b)^p $ and
$ (a + b)^p + (a - b)^p $ . . . . . . . 96--103
Surajit Rajagopal and
Martin Griffiths 98.01 On Fibonacci numbers that are
factorials . . . . . . . . . . . . . . . 104--107
Emrys Read 98.02 On integer triangles . . . . . . . 107--112
B. Sury 98.03 Explicit solutions of $ \phi (m) =
k! $ . . . . . . . . . . . . . . . . . . 112--114
J. A. Scott 98.04 A nested radical for the Euler
constant . . . . . . . . . . . . . . . . 114--116
J. A. Scott 98.05 Another minimum for the triangle 116--117
Grégoire Nicollier 98.06 The relative size of the squares
inscribed in a triangle . . . . . . . . 117--119
John Michael McNamee 98.07 The order of convergence of
Newton's Method in special cases . . . . 119--120
Nick Lord 98.08 The moment of inertia of an
elliptical wire . . . . . . . . . . . . 121--125
Nick Lord Prime numbers and the sequences $ 6 n
\pm 1 $ . . . . . . . . . . . . . . . . 126--128
Michael Sewell Areas of Lunes . . . . . . . . . . . . . 129--131
K. B. Subramaniam `Summing squares' by counting cubes . . 131--132
Anonymous Feedback . . . . . . . . . . . . . . . . 133--135
Nick Lord Problem Corner . . . . . . . . . . . . . 136--142
Stan Dolan Student Problems . . . . . . . . . . . . 143--145
John Baylis Book Review: \booktitleElements of
advanced mathematics (3rd edn.) by
Steven G. Krantz. Pp. 351. \pounds 44.99
(hbk). 2012. ISBN: 978-1-4398-9834-5
(CRC Press) . . . . . . . . . . . . . . 146--147
Gerry Leversha Book Review: \booktitleMagnificent
mistakes in mathematics, by Alfred S
Posamentier and Ingmar Lehmann. Pp. 296.
\$24 (hbk). 2013.ISBN 978-1-61614-747-1
(Prometheus Books)} . . . . . . . . . . 148--150
Gerry Leversha Book Review: \booktitlePoor Robin's
prophesies, by Benjamin Wardhaugh. Pp.
248. \pounds 14.99 (hbk). 2012, ISBN
978-0-19-960542-2 (Oxford University
Press) . . . . . . . . . . . . . . . . . 150--151
Gerry Leversha Book Review: \booktitleThe cult of
Pythagoras: math and myths by Alberto A.
Martinez. Pp. 264. \$27.95 (hbk)}},
2012. ISBN 978-0-8229-4418-8 (University
of Pittsburg Press)} . . . . . . . . . . 151--152
Michael De Villiers Book Review: \booktitleIris Runge: A
life at the crossroads of mathematics,
science and industry, by Renate Tobies.
Pp. 442. \pounds 99.00 (Hardback). 2012.
ISBN: 978-3-0348-0229-1 (Birkhauser) . . 152--155
Gerry Leversha Book Review: \booktitleThe history of
mathematics, a very short introduction,
by Jacqueline Stedall. Pp. 123. \pounds
7.99. 2012. ISBN: 978-0-19-959968-4
(Oxford University Press) . . . . . . . 155--156
Gerry Leversha Book Review: \booktitleSophie's diary,
by Dora Musielak. Pp. 291. \$68.95
(hardback). 2012. ISBN: 978-88385-577-5
(Mathematical Association of America)} 156--157
Kiril Bankov Book Review: \booktitleWhy cats land on
their feet? And 76 other physical
paradoxes and puzzles, by Mark Levi. Pp.
190. US \$19.95, 2012. ISBN
978-0-691-14854-0 (Princeton University
Press)} . . . . . . . . . . . . . . . . 157--158
Martin Griffiths Book Review: \booktitleMathematics of
life: unlocking the secrets of
existence, by Ian Stewart. Pp. 358.
\pounds 20.00 (Hardback). 2011. ISBN:
978-1-84668-198-1 (Profile) . . . . . . 158--159
Martin Griffiths Book Review: \booktitle17 equations that
changed the world, by Ian Stewart. Pp.
342. \pounds 15.99. 2012. ISBN:
978-1-84668-531-6 (Profile) . . . . . . 159--160
Kiril Bankov Book Review: \booktitleThe beauty of
everyday mathematics, by Norbert
Herrmann. Pp. 138. \pounds 17.99. 2012.
ISBN 978-3-642-22103-3 (Springer) . . . 160--161
Gerry Leversha Book Review: \booktitleThe best writing
on mathematics 2011, by Mircea Pitici
(ed.). Pp. 383. \pounds 13.95. 2012.
ISBN: 978-0-691-15315-5 (Princeton
University Press) . . . . . . . . . . . 161--163
Nick Lord Book Review: \booktitleWhat's happening
in the mathematical sciences, Volume 8,
by Dana Mackenzie. Pp. 129. \pounds
17.95. 2011. ISBN 978-0-8218-4999-6
(American Mathematical Society) . . . . 163--163
P. N. Ruane Book Review: \booktitleMotifs of
mathematics: history and application of
the mediant and the Farey sequence, by
Scott B. Guthery. Pp. 243. \pounds
11.32. 2011. ISBN 978-1-4538-1057-6.
(Docent Press) . . . . . . . . . . . . . 163--164
Mark Hunacek Book Review: \booktitle$p$-adic Lie
groups, by Peter Schneider. Pp. 254.
\pounds 72.00 (hbk). 2011. ISBN:
978-3-642-21146-1 (Springer) . . . . . . 165--166
David Applebaum Book Review: \booktitleConcrete
functional calculus, by R. M. Dudley and
R. Norvaisa. Pp. 671, \pounds 90.00,
2011, ISSN 1439-7382, ISBN
978-1-4419-6949-1 (Springer Monographs
in Mathematics) . . . . . . . . . . . . 166--168
Nick Lord Book Review: \booktitleReal analysis: a
historical approach (2nd edn.), by S.
Stahl. Pp. 293. \pounds 80.50. 2011.
ISBN 978-0-470-87890-3 (Wiley) . . . . . 168--169
Peter MacGregor Book Review: \booktitleIntroduction to
differential calculus. Systematic
studies with engineering applications.
U. L. Rohde, G. C. Jain, A. K. Poddar,
A. K. Ghosh. Pp. 747. \pounds 93.50
(hbk) 2012. ISBN 978-1-118-11775-0 (John
Wiley and Sons). Introduction to
integral calculus. Systematic studies
with engineering applications. U. L.
Rohde, G. C. Jain, A. K. Poddar, A. K.
Ghosh. Pp. 402. \pounds 76.95 (hbk)
2012. ISBN 978-1-118-11776-7 (John Wiley
and Sons) . . . . . . . . . . . . . . . 169--170
John Baylis Book Review: \booktitleLimits, limits
everywhere: the tools of mathematical
analysis, by David Applebaum. pp. 200.
\pounds 19.99. 2012. ISBN:
978-0-19-964008-9 (Oxford University
Press) . . . . . . . . . . . . . . . . . 170--171
Peter Shiu Book Review: \booktitleInequalities:
Theorems, techniques and selected
problems, by Zdravko Cvetkovski. Pp.
444, \pounds 35.99 (pbk), 2012. ISBN:
978-3-642-23791-1 (Springer) . . . . . . 171--172
Niels Jacob Book Review: \booktitleElliptic partial
differential equations, volume 1:
Fredholm theory of elliptic problems in
unbounded domains, by Vitali Volpert.
Pp. 639. \pounds 90.00 (hbk). 2011.
ISBN: 978-3-0346-0536-6 (Birkhauser) . . 172--174
Mark Hunacek Book Review: \booktitleIntroduction to
representation theory, by Pavel Etingof,
Oleg Golberg, Sebastian Hensel, Tiankai
Liu, Alex Schwendner, Dmitry Vaintrob,
Elena Yudinova and Siava Gerovitch. Pp.
228, \$42.00, 2011. ISBN:
978-0-8218-4999-6 (American Mathematical
Society)} . . . . . . . . . . . . . . . 175--176
Martin Griffiths Book Review: \booktitleIntroduction to
abstract algebra (4th edn.), by W. Keith
Nicholson. Pp. 535. \pounds 90-50 (hbk).
2012. ISBN: 978-1-118-13535-8 (Wiley) 176--177
Gerry Leversha Book Review: \booktitlePtolemy through
the looking-glass, by William Wynne
Willson. Pp. 92. \pounds 13.00. 2012.
ISBN 978-0-9558042-3-6 (Garland
Publications) . . . . . . . . . . . . . 177--178
Peter Giblin Book Review: \booktitleDivided spheres,
Edward S. Popko, Pp. 509. \pounds 44.99.
2012, ISBN 978-1-4665-0429-5 (CRC Press
(an A. K.Peters Book)) . . . . . . . . . 178--179
P. N. Ruane Book Review: \booktitleApplications of
combinatorial matrix theory to Laplacian
matrices of graphs, by Jason J.
Molitierno. Pp. 405. \pounds 57.99
(Hardback). 2012. ISBN:
978-1-4398-6337-4 (CRC Press) . . . . . 179--180
David Bevan Book Review: \booktitleApplications of
combinatorial matrix theory to Laplacian
matrices of graphs, by Jason J.
Molitierno. Pp. 405. \pounds 57.99
(Hardback). 2012. ISBN:
978-1-4398-6337-4 (CRC Press) . . . . . 180--181
Martin Griffiths Book Review: \booktitle9 algorithms that
changed the future: the ingenious ideas
that drive today's computers, by John
MacCormick. Pp. 219. \$27-95 (hbk).
2012. ISBN: 978-0-691-14714-7 (Princeton
University Press)} . . . . . . . . . . . 181--182
Peter Giblin Book Review: \booktitleUnexpected
expectations, Leonard M. Warner. Pp.
204. \pounds 24.69 (hardback). 2012.
ISBN 978-1-56881-721-7 (CRC Press) . . . 182--183
John Baylis Book Review: \booktitleProbability --- A
very short introduction, by John Haigh.
Pp. 128. \pounds 7.99. 2012. ISBN
987-0-19-958848-0 (Oxford University
Press) . . . . . . . . . . . . . . . . . 183--185
Gerry Leversha Book Review: \booktitleHow to teach
relativity to your dog, by Chad Orzel.
Pp. 328. \pounds 11.99. 2012. ISBN:
978-0-465-02331-8 (Basic Books) . . . . 185--185
Peter Shiu Book Review: \booktitleAlan Turing's
system of logic: the Princeton thesis,
Andrew W. Appel (Ed.) Pp. 142. \pounds
16.95 (hbk). 2012. ISBN:
978-0-691-15574-6 (Princeton University
Press) . . . . . . . . . . . . . . . . . 186--187
Martin Griffiths Book Review: \booktitleAlgorithmic
puzzles, by Anany Levitin and Maria
Levitin. Pp. 257. \pounds 13.99. 2011.
ISBN: 978-0-19-974044-4 (Oxford
University Press) . . . . . . . . . . . 188--188
Peter Shiu Book Review: \booktitleCombinatorial set
theory: with a gentle introduction to
forcing, by Lorenz J Halbeisen. Pp. 453.
\pounds 81.00 (Hardback). 2012. ISBN:
978-1-4471-2172-5 (Springer) . . . . . . 188--190
Gerry Leversha Book Review: \booktitlePhi, the glorious
golden ratio, by Alfred S. Posamentier
and Ingmar Lehmann. Pp. 363. \$27-00.
2012. ISBN: 978-1- 61614-423-4
(Prometheus Books)} . . . . . . . . . . 191--191
Anonymous MAG volume 98 issue 541 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 98 issue 541 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
John Conway and
Alex Ryba The Steiner--Lehmus angle-bisector
theorem . . . . . . . . . . . . . . . . 193--203
Barry Lewis Runs, strings and alphabets . . . . . . 204--226
G. J. O. Jameson Inequalities for the perimeter of an
ellipse . . . . . . . . . . . . . . . . 227--234
G. J. O. Jameson A fresh look at Euler's limit formula
for the gamma function . . . . . . . . . 235--242
Keith Parramore and
Joan Stephens Two girls --- the value of information 243--249
Mark B. Villarino Quotient polynomials with positive
coefficients . . . . . . . . . . . . . . 250--255
Thomas Koshy Graph-theoretic models for the Fibonacci
family . . . . . . . . . . . . . . . . . 256--265
K. Robin McLean Conics and convexity . . . . . . . . . . 266--272
John D. Mahony Wind over tide . . . . . . . . . . . . . 273--280
Mark B. Villarino A cubic surface of revolution . . . . . 281--290
Alastair Cuthbertson Cryptic crossnumber puzzles: a setter's
perspective . . . . . . . . . . . . . . 291--303
Charles Audet Ordering 15 marbles with a three-way
scale . . . . . . . . . . . . . . . . . 304--316
Stan Dolan 98.09 Nint reciprocity . . . . . . . . . 317--319
Des MacHale 98.10 Associativity of symmetric set
difference . . . . . . . . . . . . . . . 319--320
J. R. Nurcombe 98.11 Rearranging the signs of the
alternating harmonic series . . . . . . 321--324
J. A. Scott 98.12 A convergent series with zero sum 325--327
Tim Jameson 98.13 Some double series related to $
\zeta (3) $ . . . . . . . . . . . . . . 327--331
J. A. Scott 98.14 An unexpected closed form . . . . 331--332
István Mez\Ho 98.15 A class of dense subsets on the
real line . . . . . . . . . . . . . . . 332--334
Michael De Villiers 98.16 A variation of Miquel's theorem
and its generalisation . . . . . . . . . 334--339
Jeremy D. King and
Nick Lord 98.17 The return of the returning
explorer . . . . . . . . . . . . . . . . 339--342
J. A. Scott 98.18 Another look at the
orthocentroidal disc . . . . . . . . . . 343--345
K. B. Subramaniam 98.19 A new proof that the rationals are
countable . . . . . . . . . . . . . . . 345--345
Nick Lord A non-calculator challenge: show that $
\ln 2 < 1 \sqrt {2} $ . . . . . . . . . . 346--346
Nick Lord Evaluating $ \sum_1^n r^2 $ and $
\sum_1^n r(r + 1) $ using moments . . . 346--347
Nick Lord Discrete random variables having equal
mean and variance . . . . . . . . . . . 347--349
Nick Lord Cubics whose vertical translates
factorise . . . . . . . . . . . . . . . 349--350
Jim Dickson and
Nick Lord Approximate constructions of 1 radian 350--353
Tim Jameson Orbits made easy by complex numbers . . 353--355
Anonymous Feedback . . . . . . . . . . . . . . . . 356--357
Nick Lord Problem Corner . . . . . . . . . . . . . 358--366
Stan Dolan Student Problems . . . . . . . . . . . . 367--369
Peter MacGregor Book Review: \booktitleThe shape of
inner space, by Shing-Tung Yau and Steve
Nadis. Pp. 377. \$18.99. 2010. ISBN
978-0-465-02837-5 (Basic Books)} . . . . 370--370
Peter Hall Book Review: \booktitleEdexcel A level
maths Core 1: Students' support
material, by John Berry and Sue Langham.
Pp. 102. \pounds 5.99. 2012. ISBN
978-0-00-747601-5 (Collins) . . . . . . 370--371
Gerry Leversha Book Review: \booktitleThe secrets of
triangles, by Alfred S. Posamentier and
Ingmar Lehmann, Pp. 385, \$26. 2012.
ISBN 978-1-61614-587-3. (Prometheus
Books)} . . . . . . . . . . . . . . . . 371--373
Graham Hoare Book Review: \booktitleMathematics, an
illustrated history of numbers, Tom
Jackson (ed). Pp. 144. \pounds 20. 2012.
ISBN 978-1-84931-066-6 (Worth Press) . . 373--374
Owen Toller Book Review: \booktitleSeduced by logic
--- Émilie du Châtelet, Mary Somerville
and the Newtonian revolution, by Robyn
Arianrhod. Pp. 338. \pounds 18.99,
(hbk). 2012. ISBN 978-0-19-993161-3
(Oxford University Press) . . . . . . . 375--375
S. C. Coutinho Book Review: \booktitleCollected papers
of C. S. Seshadri volume 1: Vector
bundles and invariant theory, volume 2:
Schubert geometry and representation
theory, edited by Vikraman Balaji, V.
Lakshmibai, M. Pavaman Murthy and Madhav
V. Nori. Pp. 1008, 633 Price \$195 2012.
ISBN: 978-93-80250-17-5; (2 volume set),
(Hindustan Book Agency, New Delhi)} . . 376--377
Michael De Villiers Book Review: \booktitleIntroduction to
differential equations using Sage, by
David Joyner and Marshall Hampton. Pp.
264. \$60 (USD). 2012. ISBN
978-1-4214-0637-4, e-ISBN
978-1-4214-0724-1 (Baltimore, MD: The
John Hopkins University Press)} . . . . 377--377
Colin Foster Book Review: \booktitleHow to study for
a mathematics degree, by Lara Alcock,
pp. 288, \pounds 12.99, ISBN
978-0-19-966132-9, Oxford University
Press (2013) . . . . . . . . . . . . . . 377--378
P. G. MacGregor Book Review: \booktitleMagnificent
Principia --- exploring Isaac Newton's
masterpiece, by Colin Pask. Pp. 528.
\pounds 16.05. 2013. ISBN
978-1-61614-745-7 (Prometheus Books) . . 378--379
John Baylis Book Review: \booktitleThe great
mathematical problems, by Ian Stewart.
Pp. 340. \pounds 15.99. 2013. ISBN:
978-1-84668-1998 (Profile Books) . . . . 379--381
Gerry Leversha Book Review: \booktitleCombinatorics:
ancient and modern, edited by Robin
Wilson and John J. Watkins. Pp. 381.
\pounds 55. hardcover. 2013, ISBN
978-0-19-965659-2 (Oxford University
Press) . . . . . . . . . . . . . . . . . 381--382
Anonymous MAG volume 98 issue 542 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 98 issue 542 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b4
Peter Ransom Triumphs and Tribulations in Teaching 386--395
Helen Christian and
Brian Trustrum If everyone wanted girls more boys might
be born . . . . . . . . . . . . . . . . 396--401
A. C. Paseau and
Michael de Villiers and
Michael Fox The `stop after $k$ girls or $N$
children' policy . . . . . . . . . . . . 402--423
Juan Pla On some subsets of the rational
solutions of the equations $ a X^2 + b X
Y + c Y^2 = d Z^2 $ . . . . . . . . . . 424--428
Thomas J. Osler and
Sky Waterpeace Vieta's product for pi from the
Archimedean algorithm . . . . . . . . . 429--431
Tony Crilly and
Colin R. Fletcher Triangles meeting triangles . . . . . . 432--451
Randall Baumback Fingers find Fermat's factorisation most
probable . . . . . . . . . . . . . . . . 452--458
Nick Lord Beyond the Basel problem: Euler's
derivation of the general formula for $
\zeta (2 n) $ . . . . . . . . . . . . . 459--474
Owen Toller Statistics education: fit for purpose? 475--478
Michael Hardy Notes 98.20 A concrete view of Euclid's
proof of the infinitude of primes . . . 479--481
Nick Lord 98.21 Euclid numbers are free from
powers . . . . . . . . . . . . . . . . . 482--483
A. M. Fink 98.22 Polynomials with all real roots 483--483
Thomas J. Osler and
Tirupathi R. Chandrupatla 98.23 Recursive formulas related to the
Arithmetic--Geometric Mean . . . . . . . 484--486
J. A. Scott 98.24 An intriguing inequality . . . . . 487--488
Peter Giblin 98.25 An ancient approximation to the
sine function . . . . . . . . . . . . . 488--490
Christopher Ormell 98.26 Algorithms for $ | x | $ and $ [x]
$ . . . . . . . . . . . . . . . . . . . 490--492
J. R. Nurcombe 98.27 Necessary conditions for the
convergence of series of positive terms 493--496
Peter Shiu 98.28 If $ e < 2 $ then $ \pi $ is
irrational . . . . . . . . . . . . . . . 497--501
Kung-Wei Yang 98.29 Symmetry of continued fraction for
$ \sqrt {d} $ . . . . . . . . . . . . . 501--503
A. M. Fink 98.30 The isoperimetric inequality for
quadrilaterals . . . . . . . . . . . . . 504--504
Colin Foster 98.31 Equal volumes of revolution . . . 504--507
Grégoire Nicollier 98.32 Triangles with two angles in the
ratio $ 1 \colon 2 $ . . . . . . . . . . 508--509
Sava Grozdev and
Deko Dekov 98.33 Computer-generated mathematics:
points on the Kiepert hyperbola . . . . 509--511
David L. Farnsworth and
Michael E. Long 98.34 The definition of the sample
variance . . . . . . . . . . . . . . . . 511--517
Walter Jacob and
Thomas J. Osler 98.35 A novel approach to finding $ \int
\csc x \, d x $ . . . . . . . . . . . . 518--519
Paul G. Williams Leaving the variance unchanged . . . . . 520--525
Nick Lord A fallacy involving similar
quadrilaterals . . . . . . . . . . . . . 525--527
Anonymous On 87.24: Paul Stephenson writes . . . . 528--530
Anonymous On Fortuitous functions: The GCHQ
Problem Solving Group writes . . . . . . 531--532
Anonymous On the largest outscribed equilateral
triangle: Nick Lord writes . . . . . . . 533--534
Anonymous On 98.05: Nick Lord writes . . . . . . . 534--534
Anonymous On 98.15: Alan Beardon writes . . . . . 534--535
Nick Lord Problem Corner . . . . . . . . . . . . . 536--542
Stan Dolan Student Problems . . . . . . . . . . . . 543--545
Anonymous 55th International Mathematical
Olympiad, Cape town, 3--13 July 2014 . . 546--546
Anonymous In the pipeline for March 2015 . . . . . 546--546
Graham Storr Book Review: \booktitleHow to study for
a mathematics degree by Lara Alcock, pp.
288, \pounds 12.99, ISBN
978-019-966132-9, Oxford University
Press (2013) . . . . . . . . . . . . . . 547--547
Michael de Villiers Book Review: \booktitleTeaching
problem-solving in undergraduate
mathematics by M.S. Badger, C.J. Sangwin
and T.O. Hawkes with R.P. Burns, J.
Mason and S. Pope, pp 142, \pounds 5.25
plus postage . . . . . . . . . . . . . . 547--549
Gerry Leversha Book Review: \booktitleOxford figures:
eight centuries of the mathematical
sciences by John Fauvel, Raymond Flood
and Robin Wilson (eds), pp 406, \pounds
39.99, ISBN 978-0-19-968197-6, Oxford
University Press (2013) . . . . . . . . 549--550
Graham H. Storr Book Review: \booktitleMaster class in
mathematics education: international
perspectives on teaching and learning
edited by Paul Andrews and Tim Rowland,
pp 223, \pounds 24.99, ISBN
978-1-4411-7975-3, Bloomsbury (2014) . . 550--551
Owen Toller Book Review: \booktitleTranscending
tradition: Jewish mathematicians in
German-speaking academic culture edited
by Birgit Bergmann, Moritz Epple and
Rudi Ungar, pp 290, \pounds 35.99
(hard), \pounds 29.99 (e-book), ISBN
978-3-642-22463-8 (hard),
978-3-642-22464-5 (ebook), Springer
Verlag (2013) . . . . . . . . . . . . . 551--552
A. C. Paseau Book Review: \booktitleL. E. J. Brouwer:
Topologist, intuitionist, philosopher by
Dirk van Dalen, pp 875, \pounds 18.99,
ISBN 978-1-4471-4615-5, Springer-Verlag
(2013) . . . . . . . . . . . . . . . . . 552--554
Gerry Leversha Book Review: \booktitleLove and Math by
Edward Frankel, pp 292, \pounds 18.99,
ISBN 978-0-465-05074-1, Basic Books
(2013) . . . . . . . . . . . . . . . . . 554--555
Gerry Leversha Book Review: \booktitleThe best writing
on mathematics 2012 edited by Mircea
Pitici, pp 288, \pounds 13.95, ISBN
978-0-691-15655-2, Princeton University
Press (2013) . . . . . . . . . . . . . . 556--557
Martin Griffiths Book Review: \booktitleEuropean success
stories in industrial mathematics by T.
Lery, M. Primicerio, M.J. Esteban, M.
Fontes, Y. Maday, V. Mehrmann, G.
Quadros, W. Schilders, A. Schuppert and
H. Tewkesbury, pp 135, \pounds 44.99,
ISBN 978-3-642-23847-5, Springer (2012) 558--558
Graham H. Storr Book Review: \booktitleThe mathematical
sciences in 2025 by National Research
Council, pp 205, \pounds 32.00, ISBN
978-0-309-28457-8, The National
Academies Press (2013) . . . . . . . . . 558--559
Peter Shiu Book Review: \booktitleNumber, shape,
and symmetry: an introduction to number
theory, geometry and group theory by
Diane L. Herrmann and Paul J. Sally Jr,
pp 426, \pounds 44.99, ISBN
978-1-4665-5464-1, AK Peters, CRC Press
(2012) . . . . . . . . . . . . . . . . . 559--560
René L. Schilling Book Review: \booktitleMeasure and
integration: Publications 1997-2011 by
Heinz König, pp 512, \pounds 85.50,
\$129.00, EUR101.60, ISBN
978-3-0348-0381-6, Birkh{\"a}user
(2012)} . . . . . . . . . . . . . . . . 561--561
P. N. Ruane Book Review: \booktitleHeavenly
mathematics: the forgotten art of
spherical trigonometry by Glen Van
Brummelen, pp 192, \pounds 24.95, ISBN
978-0-691-14892-2, Princeton University
Press (2013) . . . . . . . . . . . . . . 561--562
Gerry Leversha Book Review: \booktitleBeautiful
geometry by Eli Maor and Eugen Jost, pp
187, \pounds 19.95 (hbk), ISBN
978-0-691-15099-4, Princeton University
Press (2014) . . . . . . . . . . . . . . 562--563
Peter MacGregor Book Review: \booktitleAdvanced
mechanics, by S.G. Rajeev. Pp 163. 2013.
ISBN 978-0-19-967085-7 \pounds 45.00
(hbk), \pounds 21.99 (pbk). ISBN:
978-0-19-967086-4 (Oxford University
Press) . . . . . . . . . . . . . . . . . 563--564
Owen Toller Book Review: \booktitleLooking at
numbers, by Tom Johnson and Franck
Jedrzejewski. Pp 120. \pounds 76.50.
2014. ISBN 978-3-0348-0553-7 (Birkhäuser) 564--564
Gerry Leversha Book Review: \booktitleNaked statistics,
by Charles Wheelan. Pp. 269. \pounds
18.99. 2013. ISBN 978-0-393-07195-5.
(W.W.Norton) . . . . . . . . . . . . . . 564--567
Graham Hoare Book Review: \booktitleThree views of
logic by Donald W. Loveland, Richard E.
Hodel and S.G. Sterrett, pp 344, \pounds
34.95, ISBN 978-0-691-16044-3, Princeton
University Press (2014) . . . . . . . . 567--568
Dave Applebaum Book Review: \booktitleStochastic
analysis and diffusion processes by G.
Kallianpur and P. Sundar, pp 352,
\pounds 65 (hbk), \pounds 29.99 (pbk)
ISBN 978-0-965706-3, ISBN
978-0-965707-0, Oxford Graduate Texts in
Mathematics 24, Oxford University Press
(2014) . . . . . . . . . . . . . . . . . 568--570
Stephen Rout Book Review: \booktitleA problem
solver's handbook. A guide to
intermediate mathematical olympiads,
Andrew Jobbings. Pp. 264. \pounds 14
(pbk) ISBN: 978-1-90600-1193 (UKMT) . . 570--572
Nick Lord Book Review: \booktitleMore problem
solving --- the creative side of
mathematics by Derek Holton, pp 256,
\pounds 14.99, \pounds 11.99 (MA
members), ISBN 978-0-906588-78-9, The
Mathematical Association (2013) . . . . 573--574
Anonymous Books Received . . . . . . . . . . . . . 574--574
Anonymous Acknowledgements . . . . . . . . . . . . 575--575
Gerry Leversha Request for referees . . . . . . . . . . 575--575
Anonymous The Mathematical Association . . . . . . 576--576
Anonymous MAG volume 98 issue 543 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 98 issue 543 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b2
Gerry Leversha Editorial . . . . . . . . . . . . . . . 1--1
Mowaffaq Hajja Some open problems in concurrences . . . 2--10
G. J. O. Jameson Counting Divisors . . . . . . . . . . . 11--20
Ben Eggleston The number of preference orderings: a
recursive approach . . . . . . . . . . . 21--32
Stephan Berendonk Proving the loneliness of the Khajuraho
square . . . . . . . . . . . . . . . . . 33--39
John D. Mahony Piecing it together . . . . . . . . . . 40--44
Elias Abboud On the Routh-Steiner theorem and some
generalisations . . . . . . . . . . . . 45--53
Dragu Atanasiu and
Piotr Mikusi\'nski An elementary operational calculus . . . 54--59
Martin Griffiths Random walks arising from a
Fibonacci's-rabbits scenario . . . . . . 60--67
G. J. O. Jameson A simple proof of Stirling's formula for
the gamma function . . . . . . . . . . . 68--74
Anonymous In the pipeline for July 2015 . . . . . 74--74
G. J. O. Jameson Euler--Maclaurin, harmonic sums and
Stirling's formula . . . . . . . . . . . 75--89
A. F. Beardon Removing a vertex from a tetrahedron . . 90--96
Peter Shiu Fermat's method of factorisation . . . . 97--103
Peter Shiu The factorisation of $ 2^{67} - 1 $ . . 104--108
Andrew Jobbings Where is the centre of a polygon? . . . 109--120
Samantha Caesar 99.01 Intercepts and turning points of
polynomial functions . . . . . . . . . . 121--125
Martin Griffiths 99.02 Series involving fixed-column
decimal representations . . . . . . . . 125--128
Nick Lord 99.03 Quick proofs that certain sums of
fractions are not integers . . . . . . . 128--130
Martin Griffiths and
Des MacHale 99.04 Another irrational number . . . . 130--133
Graham Jameson and
Nick Lord and
James McKee 99.05 An inequality for $ \Si (x) $ . . 133--139
Gleb Glebov 99.06 A peculiar proof of an identity of
Euler . . . . . . . . . . . . . . . . . 139--143
Nick MacKinnon 99.07 On products of factorials . . . . 144--149
Philip Todd 99.08 A mechanical `proof' of the
largest outscribed equilateral triangle 149--151
Dao Thanh Oai 99.09 A family of Napoleon triangles
associated with the Kiepert
configuration . . . . . . . . . . . . . 151--153
K. B. Subramaniam 99.10 Proof without words: $ T_1 + T_2 +
\cdots + T_n = \binom {n + 2}{3} $ . . . 153--154
B. Grivoyannis and
R. Viglione 99.11 Proof without words: A problem on
three squares . . . . . . . . . . . . . 154--154
Nick Lord Extending the parity proof that $ \sqrt
2 $ is irrational . . . . . . . . . . . 155--155
Nick Lord Areas of images of singular $ 3 \times 3
$ matrix transformations . . . . . . . . 155--156
Anonymous Feedback . . . . . . . . . . . . . . . . 157--164
N. J. L. Problem Corner . . . . . . . . . . . . . 165--170
Stan Dolan Student Problems . . . . . . . . . . . . 171--174
Gerry Leversha Dr John Frankland Rigby . . . . . . . . 174--175
Peter Hall Book Review: \booktitleCambridge
Additional Mathematics by Michael Haese,
Sandra Haese, Mark Humphries, Chris
Sangwin, pp. 504 (paper), AU\$50.00},
ISBN 978-1-92197-242-3, Haese
Mathematics (2014)} . . . . . . . . . . 176--176
Peter Hall Book Review: \booktitleCambridge
Additional Mathematics by Michael Haese,
Sandra Haese, Mark Humphries, Chris
Sangwin, pp. 504 (paper), AU\$50.00},
ISBN 978-1-92197-242-3, Haese
Mathematics (2014)} . . . . . . . . . . 176--176
Owen Toller Book Review: \booktitleCount like an
Egyptian by David Reimer, pp 237 (hbk),
\pounds 19.95, ISBN 978-0-691-16012-2,
Princeton University Press (2014) . . . 176--177
Nick Lord Book Review: \booktitleEnlightening
symbols: a short history of mathematical
notation and its hidden powers by J.
Mazur, pp. 285, \pounds 19.95, ISBN
978-0-691-15463-3, Princeton University
Press (2014) . . . . . . . . . . . . . . 177--178
Kevin J. Davis Book Review: \booktitleThe
Siddhant\=asundara of Jñ\=anar\=aja, an
English translation by Toke Lindegaard
Knudsen, pp. 351, \pounds 58.00, ISBN
013 978-1-4214-1442-3, John Hopkins
University Press (2014) . . . . . . . . 178--180
Peter Shiu Book Review: \booktitleLinear integral
equations (3rd edn.) by Rainer Kress, pp
412, \pounds 53.99 (hbk), ISBN
978-1-4614-9592-5, also available as
e-book, Springer (2014) . . . . . . . . 180--181
John Baylis Book Review: \booktitleEveryday calculus
--- discovering the hidden math all
around us by Oscar E. Fernandez, pp.
150, \pounds 16.95 (hard), ISBN
978-0-691-15755-9, Princeton University
Press (2014) . . . . . . . . . . . . . . 181--182
Mark Hunacek Book Review: \booktitleCyclic modules
and the structure of rings by S. K.
Jain, Ashish K. Srivastava and Askar A.
Tuganbaev, pp 232, \pounds 68 (hbk),
ISBN 978-0-19666-541-1, Oxford
University Press (2012) . . . . . . . . 182--183
Peter Shiu Book Review: \booktitleBasic modern
algebra with applications by Mahima
Ranjan Adhikari and Avishek Adhikari, pp
637, \pounds 42.99 (hbk), ISBN
978-81-322-1598-1, also available as
e-book, Springer (2014) . . . . . . . . 183--185
Michael Fox Book Review: \booktitleThe geometry of
the triangle by Gerry Leversha, pp. 573,
\pounds 22, ISBN 978-1-906001-17-9, The
United Kingdom Mathematics Trust (2013) 185--186
John Haigh Book Review: \booktitleJanus-faced
probability by Paolo Rocchi, pp 147,
\pounds 60.99 (hbk), ISBN
978-3-319-04860-4, Springer Verlag
(2014) . . . . . . . . . . . . . . . . . 187--187
Peter Shiu Book Review: \booktitleIntroduction to
abstract algebra by Benjamin Fine,
Anthony M. Gaglione & Gerhard
Rosenberger, pp. 566, \pounds 64.60
(hard), ISBN 978-1-4214-1176-7, Johns
Hopkins University Press (2014) . . . . 187--189
Owen Toller Book Review: \booktitlePadlock
challenges, using number and algebra by
Rachel Horsman, pp 80 (paper), \pounds
7.59 (members), \pounds 9.99
(non-members), ISBN 978-0-906588-79-6,
The Mathematical Association (2013).
Padlock challenges, statistics and
probability by Rachel Horsman, pp 72
(paper), \pounds 7.59 (members), \pounds
9.99 (non-members), ISBN
978-0-906588-80-2, The Mathematical
Association (2014) . . . . . . . . . . . 189--190
Nick Lord Book Review: \booktitleQuand les
mathématiques posent probl\`eme(s) by
Michel Bataille, pp. 216, EUR19, ISBN
978-2-7298-86738, Ellipses
www.editions-ellipses.fr (2014) . . . . 190--191
Gerry Leversha Reviewers Needed . . . . . . . . . . . . 191--192
Anonymous MAG volume 99 issue 544 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 99 issue 544 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b2
Geoffrey Howson Douglas Arthur Quadling 1926--2015 . . . 193--195
David K. Neal and
Dustin Gentile Crapoulette: card craps with one deck 196--204
Alan F. Beardon and
Paul Stephenson The Heron parameters of a triangle . . . 205--212
Des Machale and
Joseph Manning Maximal runs of strictly composite
integers . . . . . . . . . . . . . . . . 213--219
Thomas J. Osler Short and fuzzy derivations of five
remarkable formulas for primes . . . . . 220--225
Michael Sewell Parametric Envelopes . . . . . . . . . . 226--229
Glyn George When copycats lose . . . . . . . . . . . 230--236
Martin Josefsson Minimal area of a bicentric
quadrilateral . . . . . . . . . . . . . 237--242
Trygve Breiteig Quotients of triangular numbers . . . . 243--255
Victor Oxman and
Moshe Stupel Elegant special cases of Van Aubel's
theorem . . . . . . . . . . . . . . . . 256--262
Imre Patyi On some elementary functions . . . . . . 263--275
G. J. O. Jameson Sine, cosine and exponential integrals 276--289
John Baylis Why avoid induction? . . . . . . . . . . 290--297
C. J. Sangwin An audited elementary algebra . . . . . 298--316
Emrys Read 99.12 Primitive integer triangles . . . 317--319
W. J. A. Colman 99.13 Solving the quintic in radicals 319--323
Rob Downes 99.14 A recurrence relation for the
limit point of nested triangles . . . . 323--325
Nick Lord 99.15 Triangles in which $ a^n = b^n +
c^n $ . . . . . . . . . . . . . . . . . 326--328
Dong Jun Jee and
Tuo Yeong Lee and
Nathaniel Zhi-Wei Leon 99.16 Conditionally convergent series 328--331
Martin Griffiths 99.17 Irrational sums from reciprocals
of factorials . . . . . . . . . . . . . 331--335
Nick Lord 99.18 Justifying the $ \sqrt {2 \pi } $
factor in Stirling's formula . . . . . . 336--337
Nick Lord 99.19 When do the inradius and exradii
form progressions? . . . . . . . . . . . 337--339
Geoff Smith 99.20 A projective Simson line . . . . . 339--341
Mowaffaq Hajja 99.21 The simplest proof ever of the \em
pons asinorum theorem . . . . . . . . . 341--342
Martin Griffiths 99.22 The golden ratio and equilateral
triangles . . . . . . . . . . . . . . . 342--346
Philip W. Kuchel 99.23 Kicking a cube . . . . . . . . . . 346--347
Jonny Griffiths 99.24 The Not-on-the-line transformation 347--352
Jeremy D. King 99.25 The work done by friction . . . . 352--356
Shikha Chandrashekhar 99.26 Proof without words: $ \csc {2 x}
= \cot x - \cot {2 x} $ . . . . . . . . 357--357
Stan Dolan Complex numbers and triangles . . . . . 357--358
Nick Lord A rich calculus problem about a frustum 359--362
John D. Mahony Correspondence . . . . . . . . . . . . . 363--363
Anonymous Feedback . . . . . . . . . . . . . . . . 363--367
N. J. L. Problem Corner . . . . . . . . . . . . . 368--375
Stan Dolan Student Problems . . . . . . . . . . . . 376--378
Stan Dolan The School Mathematics Project
1961--1970, a decade of innovation and
its sequel by Bryan Thwaites, Cambridge
University Press, available free from
the author. . . . . . . . . . . . . . . 379--380
Owen Toller Book Review: \booktitleOrigins of
mathematical words by Anthony Lo Bello,
pp 350, \$32.00 (paper), ISBN
978-1-4214-1098-2, Johns Hopkins
University Press (2013)} . . . . . . . . 380--381
Peter MacGregor Book Review: \booktitleWizards, aliens
and starships by Charles L. Adler, pp.
378, \pounds 29.95 (hard), ISBN
978-0-691-14715-4, Princeton University
Press (2014) . . . . . . . . . . . . . . 381--382
Owen Toller Book Review: \booktitleCalculus for the
ambitious by T. W. Körner, pp 165,
\pounds 17.99 (hard), ISBN
978-1-107-06392-1, Cambridge University
Press (2014) . . . . . . . . . . . . . . 382--383
Owen Toller Book Review: \booktitleProfessor
Stewart's casebook of mathematical
mysteries by Ian Stewart, pp. 307.
\$16.99 (paper), ISBN 978-0-465-05497-8,
Basic Books (2014)} . . . . . . . . . . 383--383
Anonymous MAG volume 99 issue 545 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 99 issue 545 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Lynne McClure Looking backward, looking forward . . . 386--390
Ruth Merttens Textbooks from Shanghai and Singapore: A
National Debate . . . . . . . . . . . . 391--401
Tony Crilly and
Colin R. Fletcher The `hitchhiker triangle' and the
problem of perimeter = area . . . . . . 402--415
Nigel Derby A search for sums of powers . . . . . . 416--421
I. Ferit Öktem On the product $ \prod_{n = 2}^\infty
\zeta (n) $ . . . . . . . . . . . . . . 422--426
Martin Griffiths A slowly converging sequence via
Pythagoras . . . . . . . . . . . . . . . 427--431
Stan Dolan Triangles around a given triangle . . . 432--443
John Sharp Artzt parabolas of a triangle . . . . . 444--463
Martin Griffiths The carry-on-until-one-girl proportion 464--467
Michael Sewell An octet of circles . . . . . . . . . . 468--473
Mark B. Villarino A Tripos surd . . . . . . . . . . . . . 474--480
Aldo Scimone Ellipse: what else? . . . . . . . . . . 481--490
G. J. O. Jameson Evaluating Fresnel-type integrals . . . 491--498
Raymond A. Beauregard and
Vladimir A. Dobrushkin Differential equations v. power series 499--503
P. K. Aravind Variations on a sangaku problem
involving kissing spheres . . . . . . . 504--515
Russell Euler 99.27 A relationship between Pell
numbers and triangular square numbers 516--516
Varun Amar Reddy 99.28 A generalisation of an intriguing
ratio . . . . . . . . . . . . . . . . . 516--522
Martin Griffiths 99.29 On the sum of the reciprocals of
the primorials . . . . . . . . . . . . . 522--523
Kung-Wei Yang 99.30 The positive eigenvector of a
positive matrix . . . . . . . . . . . . 523--525
Grégoire Nicollier 99.31 A generalisation of Proizvolov's
identity . . . . . . . . . . . . . . . . 525--526
J. A. Scott 99.32 On the square wave series . . . . 526--528
Panagiotis T. Krasopoulos 99.33 An integral inequality with
applications to probability theory . . . 528--530
Nick Lord 99.34 A special parallelogram . . . . . 530--532
J. A. Scott 99.35 On the asymptotes of the Kiepert
hyperbola . . . . . . . . . . . . . . . 532--533
A. F. Beardon 99.36 Stable tables . . . . . . . . . . 534--536
Andrew Buchanan and
John Conway 99.37 Anthropologic . . . . . . . . . . 537--538
K. B. Subramaniam 99.38 Proof without words: Cotangent
expressed as a series of cosecants of
multiple angles in powers of two . . . . 538--538
E. M. Sieminski and
R. Viglione 99.39 Proof without words: A delightful
water pouring problem . . . . . . . . . 538--539
Ivica Gusi\'c On the bounds for the perimeter of an
ellipse . . . . . . . . . . . . . . . . 540--541
Nick Lord Cauchy--Schwarz via collisions . . . . . 541--542
Nick Lord The constant acceleration formulae imply
constant acceleration! . . . . . . . . . 542--543
Nick Lord A rich problem on digital roots . . . . 543--545
Anonymous Feedback . . . . . . . . . . . . . . . . 545--546
N. J. L. Problem Corner . . . . . . . . . . . . . 547--554
Stan Dolan Student Problems . . . . . . . . . . . . 554--556
Owen Toller Book Review: \booktitleThe Mathematical
Association Calendar 2016, \pounds 6.99
(reductions for multiple purchases), The
Mathematical Association . . . . . . . . 557--557
Jo French Book Review: \booktitleI died for beauty
(1st edn), by Marjorie Senechal, pp 300,
\pounds 22.50 (hard), ISBN
978-0-19-973259-3, Oxford University
Press (2013) . . . . . . . . . . . . . . 557--558
Tony Crilly Book Review: \booktitleA mystic dream of
4 by Iggy McGovern, pp 92, \pounds
11.50, ISBN 978-0-9926294-0-3, Quaternia
Press (2013) . . . . . . . . . . . . . . 558--561
Graham Hoare Book Review: \booktitleTaming the
unknown: a history of algebra from
antiquity to the early twentieth century
by Victor J. Katz and Karen Hunger
Parshall, pp. 485, \pounds 34.95 (hard),
ISBN 978-0-691-14905-9, Princeton
University Press (2014) . . . . . . . . 561--562
Tony Crilly Book Review: \booktitleJohn Napier:
life, logarithms, and legacy by Julian
Havil, pp 279, \pounds 33.48, ISBN
978-0-691-15570-8, Princeton University
Press (2014) . . . . . . . . . . . . . . 562--564
Peter MacGregor Book Review: \booktitleJames Clerk
Maxwell, edited by [Raymond Flood,] Marc
McCartney and Andrew Whitaker, pp 364,
\pounds 39.99 (hard), ISBN
978-0-19-966437-5, Oxford University
Press (2014) . . . . . . . . . . . . . . 564--564
Owen Toller Book Review: \booktitleElliptic tales by
Avner Ash and Robert Gross, pp 253,
\$16.95 (paper), ISBN 978-0-691-16350-5,
Princeton University Press (2012)} . . . 564--565
Gerry Leversha Book Review: \booktitleMathematics in
20th century literature and art by
Robert Tubbs, pp 162, \pounds 19.50,
ISBN 978-1-4214-1380-8, Johns Hopkins
University Press (2014) . . . . . . . . 565--566
Gerry Leversha Book Review: \booktitleThe best writing
on mathematics 2013 edited by Mircea
Pitici, pp 244, \pounds 14.95, ISBN
978-0-691-16041-2, Princeton (2014) . . 566--567
Nick Lord Book Review: \booktitleLocally convex
spaces by M. Scott Osborne, pp 213,
\pounds 44.99 (hard), ISBN
978-3-319-02044-0, Springer Verlag
(2014) . . . . . . . . . . . . . . . . . 568--569
John Baylis Book Review: \booktitleA course in
mathematical analysis by D. J. H.
Garling, pp 939 (paper, 3 volumes,
\pounds 29.99 each), ISBN
978-1-107-61418-5, 978-1-107-67532-2,
978-1-107-66330-5, Cambridge University
Press (2013, 2014) . . . . . . . . . . . 569--570
Graham Hoare Book Review: \booktitleInterpreting
Gödel: critical essays by Juliette
Kennedy (ed), pp 279, \pounds 60 (hard),
ISBN 978-1-10-00266-1, Cambridge
University Press (2014) . . . . . . . . 570--572
S. C. Coutinho Book Review: \booktitleCondition: The
geometry of numerical algorithms by
Peter Bürgisser & Felipe Cucker, pp 554,
\pounds 79.00 (hard), ISBN
978-3-642-38895-8, Springer Verlag
(2013) . . . . . . . . . . . . . . . . . 572--574
Peter MacGregor Book Review: \booktitleGames and
mathematics by David Wells, pp 246,
\pounds 15.99 (paper), ISBN
978-1-107-69091-2, Cambridge University
Press (2012) . . . . . . . . . . . . . . 574--574
Anonymous MAG volume 99 issue 546 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 99 issue 546 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b4
John Conway and
Alex Ryba Remembering spherical trigonometry . . . 1--8
Jan Gustavsson and
Mikael P. Sundqvist Defining trigonometric functions via
complex sequences . . . . . . . . . . . 9--23
J. N. S. Matthews Should we play on your lawn or mine? . . 24--33
Richard Ellard and
Des MacHale Packing a rectangle with $ m \times (m +
1) $ rectangles . . . . . . . . . . . . 34--47
Raghavendra G. Kulkarni Picking genuine zeros of cubics in the
Tschirnhaus method . . . . . . . . . . . 48--53
Michael Fox Some properties of Kiepert lines of a
triangle . . . . . . . . . . . . . . . . 54--67
Martin Josefsson On the classification of convex
quadrilaterals . . . . . . . . . . . . . 68--85
Dale K. Hathaway and
Joshua Barks Calculus meets the birthday problem . . 86--92
G. C. Shephard Convex polygons as carriers . . . . . . 93--102
Emrys Read 100.01 Heronian triangles . . . . . . . 103--108
Pawel Jan Piskorz 100.02 Square pyramidal numbers and the
multiplication table . . . . . . . . . . 108--111
Hsuan-Chi Chen 100.03 Evaluating the probability
integral by annular partition . . . . . 111--113
J. R. Nurcombe 100.04 Converses of a `curious' theorem
of Ces\`aro on conditionally convergent
series . . . . . . . . . . . . . . . . . 113--118
Peter Shiu 100.05 Another evaluation of $ \zeta (2)
$ . . . . . . . . . . . . . . . . . . . 118--119
Vincent Ferlini 100.06 Using linear transformations to
solve quadratic equations . . . . . . . 119--124
France Dacar 100.07 Yet another proof of the
Steiner--Lehmus theorem . . . . . . . . 124--126
Nuno Luzia 100.08 Pythagoras theorem by sliding a
triangle . . . . . . . . . . . . . . . . 126--128
Grégoire Nicollier 100.09 Extremal distance ratios . . . . 129--130
Russell J. May 100.10 Dice problems with generating
function solutions . . . . . . . . . . . 131--137
Martin Griffiths 100.11 A trinomial identity from both a
tiling and an expansion . . . . . . . . 137--139
Ángel Plaza 100.12 Visual proof of the limit of
$f$-mean recurrence sequences . . . . . 139--141
Paul Stephenson 100.13 The Steinhaus `four-colour'
tiling . . . . . . . . . . . . . . . . . 141--143
John M. Mcnamee 100.14 Optimum choice of interpolation
points in Newton's divided difference
formula . . . . . . . . . . . . . . . . 143--145
Avi Sigler and
Moshe Stupel 100.15 Proof Without Words . . . . . . . 146--146
Paul Levrie and
Rudi Penne The extended Euclidean Algorithm made
easy . . . . . . . . . . . . . . . . . . 147--149
John B. Cameron Mersenne's challenge and square roots 150--152
Nick Lord When is the sum of two triangular
numbers triangular? . . . . . . . . . . 152--154
Nick Lord Constructing the 15th pentagon that
tiles the plane . . . . . . . . . . . . 154--158
James Arathoon Miet and
Kevin J. Davis Correspondence . . . . . . . . . . . . . 159--160
Anonymous Feedback . . . . . . . . . . . . . . . . 161--163
N. J. L. Problem Corner . . . . . . . . . . . . . 164--171
Stan Dolan Student Problems . . . . . . . . . . . . 172--174
Peter Hall Book Review: \booktitleHow humans learn
to think mathematically by David Tall,
pp. 457, \pounds 27.99 (paper), ISBN
978-1-107-66854-6, Cambridge University
Press (2014) . . . . . . . . . . . . . . 175--175
Nick Lord Book Review: \booktitleA readable
introduction to real mathematics by
Daniel Rosenthal, David Rosenthal and
Peter Rosenthal, pp. 161, \pounds 35.99
(hard), ISBN 978-3-319-05653-1, Springer
(2014) . . . . . . . . . . . . . . . . . 175--176
Mark Hunacek Book Review: \booktitleThe Abel Prize
2008--2012, edited by Helge Holden &
Ragni Piene, pp. 572, \pounds 59.99
(hard), ISBN 978-3-642-39448-5, also
available as e-book, Springer Verlag
(2014) . . . . . . . . . . . . . . . . . 176--178
Owen Toller Book Review: \booktitleMathematics
without apologies by Michael Harris, pp.
421, \pounds 19.95 (hard), ISBN
978-0-691-15423-7, Princeton University
Press (2015) . . . . . . . . . . . . . . 178--179
Owen Toller Book Review: \booktitleThe world of
numbers by Herbert McKay, pp. 198,
\pounds 26.99 (paper), ISBN
978-1-107-49499-2, Cambridge University
Press (2015) . . . . . . . . . . . . . . 179--180
René L. Schilling Book Review: \booktitleUpper and lower
bounds for stochastic processes, modern
methods and classical problems by Michel
Talagrand, pp. 626, \pounds 99.00
(hard), ISBN 978-3-642-54074-5, also
available as e-book, Springer Verlag
(2014) . . . . . . . . . . . . . . . . . 180--181
René L. Schilling Book Review: \booktitleA course on
integration theory by Nicolas Lerner,
pp. 492, \pounds 62.99 (paper), ISBN
978-3-0348-0693-0, also available as
e-book, Birkhäuser (2014) . . . . . . . . 181--181
Peter Shiu Book Review: \booktitleMultivariate
calculus and geometry (3rd edn.), by Seán
Dineen, pp. 257, \$36.39 (paper), ISBN
978-1-4471-6418-0, also available as
e-book, Springer Verlag (2014)} . . . . 181--182
Peter Macgregor Book Review: \booktitlePartial
differential equations, by Michael
Shearer and Rachel Levy, pp. 274,
\pounds 59.00 (hard), ISBN
978-0-691-16129-7, Princeton University
Press (2015) . . . . . . . . . . . . . . 182--183
Owen Toller Book Review: \booktitleNumbers and
functions, steps into analysis (3rd
edn.) by R.P. Burn, pp. 347, \pounds
34.99 (paper), ISBN 978-1-107-44453-9,
Cambridge University Press (2015) . . . 183--183
Peter Macgregor Book Review: \booktitleLinear algebra,
step by step by Kuldeep Singh, pp. 608,
\pounds 29.99 (paper), ISBN
978-0-19-965444-4, Oxford University
Press (2014) . . . . . . . . . . . . . . 183--184
Peter Macgregor Book Review: \booktitleTensor calculus
for physics, by Dwight E.
Neuenschwander, pp. 227, \$45.00
(paper), ISBN 978-1-421-41565-9, Johns
Hopkins University Press (2015)} . . . . 184--184
Owen Toller Book Review: \booktitleThe mathematics
of map projections (paperback edition)
by R. K. Melluish, pp. 145, \pounds
24.99 (paper), ISBN 978-1-107-65848-6,
Cambridge University Press (2014) . . . 184--185
Owen Toller Book Review: \booktitleNautical
mathematics (paperback edition) by S. A.
Watling and J. C. Hill, pp. 143, \pounds
24.99 (paper), ISBN 978-1-107-64252-2,
Cambridge University Press (2014) . . . 184--185
Dominic Yeo Book Review: \booktitleBalkan
Mathematical Olympiads by Mircea
Becheanu & Bogdan Enescupp pp. 273,
\$59.95 (hard), ISBN 978-0-98856-225-7,
XYZ Press (2014)} . . . . . . . . . . . 185--186
Nick Lord Book Review: \booktitleProblems and
proofs in numbers and algebra by R. S.
Millman, P. J. Shiue and E. B. Kahn, pp.
223, \pounds 35.99 (hard), ISBN
978-3-319-14426-9, Springer (2015) . . . 186--187
Stephen Rout Book Review: \booktitleTopics in algebra
and analysis by Radmila Bulajich
Manfrino, José Antonio Gómez Ortega and
Rogelio Valdez Delgado, pp. 303, \pounds
40.99 (paper), ISBN 978-3-319-11945-8,
Birkhauser (2015) . . . . . . . . . . . 187--189
Anonymous Books Received . . . . . . . . . . . . . 189--190
Anonymous MAG volume 100 issue 547 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 100 issue 547 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b4
John Stubbs and
Jacob Adetunji UK pension changes in 2015: some
mathematical considerations . . . . . . 193--202
Peter Shiu The mean-square value of the divisor
function . . . . . . . . . . . . . . . . 203--212
Martin Josefsson Properties of Pythagorean quadrilaterals 213--224
Fleur T. Tehrani and
Gerry Leversha A simple approach to solving cubic
equations . . . . . . . . . . . . . . . 225--232
José Luis Cereceda An alternative recursive formula for the
sums of powers of integers . . . . . . . 233--238
Geoff C. Smith Circles in areals . . . . . . . . . . . 239--246
Osvaldo Marrero What is Bayesian statistics? . . . . . . 247--256
G. J. O. Jameson Using double integrals to solve single
integrals . . . . . . . . . . . . . . . 257--265
Nick Lord Euler, the clothoid and $ \int_0^\infty
\frac {\sin x} / x \, d x $ . . . . . . 266--273
Thomas J. Osler and
Walter Jacob and
Ryo Nishimura An infinite product of nested radicals
for $ \log x $ from the Archimedean
algorithm . . . . . . . . . . . . . . . 274--278
Joseph Tonien A simple proof of Euler's continued
fraction of $ e^{1 / M} $ . . . . . . . 279--287
Peter Shiu Cyclotomy and the heptadecagon . . . . . 288--297
G. J. O. Jameson The incomplete gamma functions . . . . . 298--306
Ian Stewart Sir Erik Christopher Zeeman FRS
1925--2016 . . . . . . . . . . . . . . . 307--313
Stan Dolan 100.16 The Diophantine equation $ n (x +
y + z) = x y z $ . . . . . . . . . . . . 314
Boyko B. Bantchev 100.17 The vector triple product and
planar vector algebra . . . . . . . . . 314--317
Hsuan-Chi Chen 100.18 Newton's semicircle and the
probability integral . . . . . . . . . . 317--321
Nick Lord 100.19 A quick evaluation of $ \lim_{m
\to \infty } \sum_{k = 0}^m \left (\frac
{k}{m} \right)^m $ . . . . . . . . . . . 321--323
Jim Simons 100.20 Outside the box . . . . . . . . . 323--329
Andrew Jobbings 100.21 Generalising the arbelos . . . . 329--335
Peter Neumann Inspiring Teachers . . . . . . . . . . . 385--395
David Hopkins Will my numbers add up correctly if I
round them? . . . . . . . . . . . . . . 396--409
Antal A. Járai The dice-and-numbers game . . . . . . . 410--419
Ulrich Abel High order algorithms for calculating
roots . . . . . . . . . . . . . . . . . 420--428
Nick Lord The most elementary proof that $ \sum_{k
= 1}^\infty 1 / k^2 = \pi^2 / 6 $ . . . 429--434
Tamsin Forbes and
Tony Forbes Hanoi revisited . . . . . . . . . . . . 435--441
A. C. Paseau Letter Games: a metamathematical taster 442--449
Jonny Griffiths Identities connecting the Chebyshev
polynomials . . . . . . . . . . . . . . 450--459
Raymond A. Beauregard and
Vladimir A. Dobrushkin Multisection of series . . . . . . . . . 460--470
Thomas J. Osler Bisecting and trisecting the arc of the
lemniscate . . . . . . . . . . . . . . . 471--481
Stan Dolan Less than equable Heronian triangles . . 482--489
Geoffrey Howson Alan Richard Tammadge 9 July 1921--25
Feb 2016 . . . . . . . . . . . . . . . . 490--491
Sergiy Koshkin 100.28 Mixing angle trisection with
Pythagorean triples . . . . . . . . . . 492--495
Amrik Nimbran and
Paul Levrie 100.29 Some odd series for $ \pi $ . . . 496--500
Martin Josefsson 100.30 Generalisations of the altitude
theorem . . . . . . . . . . . . . . . . 501--505
Martin Josefsson 100.31 Heron-like formulas for
quadrilaterals . . . . . . . . . . . . . 505--508
J. A. Scott 100.32 Linear quadrisection and the
Kiepert hyperbola . . . . . . . . . . . 508--510
Russell Euler and
Jawad Sadek 100.33 A surprising relationship between
Pell--Lucas, Pell, square and centred
square numbers . . . . . . . . . . . . . 510--511
Robert Schenk 100.34 Tilings from a square template
with asymmetric edges . . . . . . . . . 511--516
Tom Edgar 100.35 Proof without words: the average
of square pyramidal and triangular is
tetrahedral . . . . . . . . . . . . . . 516--517
Tony Crilly How to play the triangle game . . . . . 1--10
John R. Silvester Extremal area ellipses of a convex
quadrilateral . . . . . . . . . . . . . 11--26
Stephan Berendonk Double generating spirographic curves 27--37
Graham Jameson and
Nick Lord Integrals evaluated in terms of
Catalan's constant . . . . . . . . . . . 38--49
Stephen Andrilli Some strategies for teaching a course
based on \booktitleGödel, Escher, Bach 50--59
Ioulia N. Baoulina and
Martin Kreh and
Jörn Steuding Deleting digits . . . . . . . . . . . . 60--68
Paul Levrie and
Amrik Singh Nimbran Recycling Stirling's series acceleration
technique . . . . . . . . . . . . . . . 69--82
Heidi Burgiel and
Mahmoud El-Hashash Open questions on Tantrix graphs . . . . 83--89
Roy Barbara 101.01 Fermat's last theorem for $ n = 3
$ revisited . . . . . . . . . . . . . . 90--93
Yannick Saouter 101.02 A (doubly) elementary formula for
prime numbers . . . . . . . . . . . . . 93--95
A. F. Beardon 101.03 Products of $ 3 \times 3 $ magic
matrices . . . . . . . . . . . . . . . . 96--98
Nick Lord 101.04 An unexpected appearance of the
golden ratio . . . . . . . . . . . . . . 98--99
Christoph Kirfel and
Rainer Kaenders 101.05 Integration by symmetry . . . . . 99--103
Seán M. Stewart 101.06 Finding some integrals using an
interesting self-similar substitution 103--108
Peter R. Mercer 101.07 Cauchy's mean value theorem meets
the logarithmic mean . . . . . . . . . . 108--115
Joseph Tonien 101.08 A continued fraction inspired by
an identity of Euler . . . . . . . . . . 115--121
Yehao Shi and
Ling Lin 101.09 A generalisation of Nesbitt
inequality . . . . . . . . . . . . . . . 122
Martin Lukarevski 101.10 Exradii of the triangle and
Euler's Inequality . . . . . . . . . . . 123
Mowaffaq Hajja 101.11 An application of a morsel of
Honsberger . . . . . . . . . . . . . . . 123--125
Mowaffaq Hajja 101.12 The sum of the squared lengths of
equally-spaced cevians . . . . . . . . . 126--128
J. A. Scott 101.13 The Lester circle once again . . 129--130
Reginald Koo 101.14 The direction of limiting
friction . . . . . . . . . . . . . . . . 130--135
M. G. Elliott Projectiles from circular motion . . . . 136--141
Nick Lord Using A4-sized paper to illustrate that
$ \sqrt {2} $ is irrational . . . . . . 142--145
Anonymous Feedback . . . . . . . . . . . . . . . . 146--149
N. J. L. Problem Corner . . . . . . . . . . . . . 150--156
Stan Dolan Student Problems . . . . . . . . . . . . 157--159
Graham Storr Book Review: \booktitleMathematics and
the body: material entanglements in the
classroom by De Freitas, Elizabeth and
Sinclair, Nathalie, pp. 284, \pounds
65.00 (hard), ISBN 978-1-107-03948-3,
Cambridge University Press (2014) . . . 160--160
Peter Hall Book Review: \booktitleLesson study,
challenges in mathematics education,
edited by Inprasitha, Maitree et al.,
pp. 377, \pounds 32 (paper), ISBN
978-98128-3541-3, World Scientific
(2015) . . . . . . . . . . . . . . . . . 160--161
Gerry Leversha Book Review: \booktitleSpecial secondary
schools for the mathematically talented:
an international panorama by Vogeli,
Bruce R. (ed), pp. 438, \pounds 134,
ISBN 978-9-81466-746-3, World Scientific
(2015) . . . . . . . . . . . . . . . . . 161--162
Kevin Davis Book Review: \booktitleMathematics in
ancient Egypt, a contextual history by
Imhausen, Annette, pp. 234, \pounds
21.05 (hard), ISBN 978-0-691-11713-3,
Princeton University Press (2016) . . . 163--165
Graham Hoare Book Review: \booktitleLeonhard Euler,
mathematical genius in the Enlightenment
by Calinger, Ronald S., pp. 669, \pounds
37.95 (hard), ISBN 978-0-691-11927-4,
Princeton University Press (2016) . . . 165--166
Martin Griffiths Book Review: \booktitleGenius at play:
the curious mind of John Horton Conway
by Roberts, Siobhan, pp. 472, \pounds
20.00 (hard), ISBN 978-1-62040-593-2,
Bloomsbury Publishing (2015) . . . . . . 167--168
Owen Toller Book Review: \booktitleL. A. Math by
Stein, James D., pp. 240, \$24.95
(hard), ISBN 978-0-69116-828-9,
Princeton University Press (2015)} . . . 168--169
Mark Hunacek Book Review: \booktitleThe Princeton
companion to applied mathematics, edited
by Higham, Nicholas J., pp. 1016,
\pounds 69.95 (hard), ISBN
978-0-691-15039-0, Princeton University
Press (2015) . . . . . . . . . . . . . . 169--170
Owen Toller Book Review: \booktitleFrom music to
mathematics, by Roberts, Gareth E., pp.
320, \$49.95 (hard), ISBN
978-1-42141-918-3, Johns Hopkins
University Press (2016)} . . . . . . . . 170--171
Bernhard Von Stengel Book Review: \booktitleJane Austen, game
theorist (updated edition), by Chwe,
Michael Suk-Young, pp 296, \pounds 15.95
(paper), ISBN: 978-0-691-16244-7,
Princeton University Press (2014) . . . 172--172
Nick Lord Book Review: \booktitleThe call of the
primes, by O'Shea, Owen, pp. 330, \$19,
ISBN 978-1-63388-148-8, Prometheus Books
(2016)} . . . . . . . . . . . . . . . . 173--174
Owen Toller Book Review: \booktitleSumming it up:
from one plus one to modern number
theory, by Ash, Avner and Gross, Robert,
pp. 229, \$27.95 (hard), ISBN
978-0-691-17019-0, Princeton University
Press (2016)} . . . . . . . . . . . . . 174--175
Mark Hunacek Book Review: \booktitleA course in
analysis, by Jacob, Niels and Evans,
Kristian P., pp. 744, \pounds 43
(paper), ISBN 987-9814-68909-0, World
Scientific Publishing Co (2015) . . . . 175--177
John Baylis Book Review: \booktitleAlgebra in
context, by Shell-Gellasch, Amy and
Thoo, J. B., pp. 536, \pounds 80.50
(hard), ISBN 978-14214-1728-9, Johns
Hopkins Press (2015) . . . . . . . . . . 177--179
S. C. Coutinho Book Review: \booktitleCondition: The
geometry of numerical algorithms, by
Bürgisser, Peter & Cucker, Felipe, pp 554,
\pounds 79.00 (hard), ISBN
978-3-642-38895-8, Springer Verlag
(2013) . . . . . . . . . . . . . . . . . 179--181
Owen Toller Book Review: \booktitleChancing it, by
Matthews, Robert, pp. 290, \pounds 14.99
(hard), ISBN 978-1-781-25030-3, Profile
Books (2015) . . . . . . . . . . . . . . 181--182
Owen Toller Book Review: \booktitleThe seven pillars
of statistical wisdom, by Stigler,
Stephen M., pp. 230, \pounds 16.95
(paper), ISBN 978-0-674-08891-7, Harvard
University Press (2016) . . . . . . . . 182--183
Owen Toller Book Review: \booktitleTeaching
probability, by Gage, Jenny and
Speigelhalter, David, pp. 197, \pounds
17.95 (paper), ISBN 978-1-316-60589-9,
Cambridge University Press (2016) . . . 183--184
Robert Leek Book Review: \booktitleThe logic of
infinity, by Sheppard, Barnaby, pp 473,
\pounds 27.99 (paper), ISBN
978-1-107-67866-8, Cambridge University
Press (2014) . . . . . . . . . . . . . . 184--185
Graham Storr Book Review: \booktitleThe foundations
of mathematics (second edition), by
Stewart, Ian and Tall, David, pp. 416,
\pounds 14.99 (paper), ISBN
978-0-19870643-4, Oxford University
Press (2015) . . . . . . . . . . . . . . 185--186
Gerry Leversha Book Review: \booktitleProblem solving
tactics, by di Pasquale, A., Do, N. and
Mathews, D., pp. 304, \$A115, ISBN
978-1-87642-075-8, Australian
Mathematics Trust (2014)} . . . . . . . 186--187
Nick Lord Book Review: \booktitleProblem-solving
strategies in mathematics, by
Posamentier, A. S. & Krulik, S., pp. 163,
\pounds 20, ISBN 9-789814-651639, World
Scientific (2015) . . . . . . . . . . . 187--188
S. C. Coutinho Book Review: \booktitleElements of
numerical analysis, by Gupta, Radhey S.
(2nd edn.), pp. 759, AUD\$86.32 exc GST
(paper), ISBN 978-1-107-50049-5,
Cambridge University Press (2015)} . . . 189--189
Anonymous Books Received . . . . . . . . . . . . . 190--190
Anonymous The Mathematical Association . . . . . . 191--191
Anonymous MAG volume 101 issue 550 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 101 issue 550 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b2
Stan Dolan Lyness cycles . . . . . . . . . . . . . 193--207
Martin Josefsson Generalisation of a quadrilateral
duality theorem . . . . . . . . . . . . 208--213
Martin Josefsson Properties of bisect-diagonal
quadrilaterals . . . . . . . . . . . . . 214--226
David Treeby Finding sums of powers using physical
arguments . . . . . . . . . . . . . . . 227--235
G. J. O. Jameson Expressing harmonic sums as fractions 236--249
Jeehoon Kang Brilliance or steadiness? A suggestion
of an alternative model to Hardy's model
concerning golf (1945) . . . . . . . . . 250--260
Jonathan Hoseana Integration based on the parametrisation
of conics . . . . . . . . . . . . . . . 261--267
Seán M. Stewart Some alternative derivations of Craig's
formula . . . . . . . . . . . . . . . . 268--279
Anonymous Centenary of the birth of Bill Tutte . . 279--279
Christopher D. Hollings R. S. Ball's Mechanics: bringing Newton
to the masses? . . . . . . . . . . . . . 280--288
Robert A. Wilson 101.15 An elementary proof that not all
principal ideal domains are Euclidean
domains . . . . . . . . . . . . . . . . 289--293
Nick Lord 101.16 When does $ n! $ have $n$ digits? 293--296
Graham Jameson and
Nicholas Jameson 101.17 Goats and birds . . . . . . . . . 296--300
Paul Stephenson 101.18 Proof without words: relationship
between inverse cotangents . . . . . . . 300--300
Mieczyslaw Szyszkowicz 101.19 Approximate quadrature of the
circle using a set square . . . . . . . 301--302
John Molokach 101.20 A natural occurrence of the
Golden Ratio . . . . . . . . . . . . . . 303--303
Grégoire Nicollier 101.21 A homothetic property of orthic
triangles . . . . . . . . . . . . . . . 303--306
Mowaffaq Hajja 101.22 The hyperbolic version of the
Steiner--Lehmus theorem . . . . . . . . 306--307
Mowaffaq Hajja 101.23 One more note on the extremal
properties of the incentre and the
excentres of a triangle . . . . . . . . 308--310
Zoltan Retkes 101.24 Generalisation and sharpening of
Problem 100.C . . . . . . . . . . . . . 310--313
Martin Griffiths 101.25 A note on tilings and associated
linear recurrences . . . . . . . . . . . 314--318
Martin Celli Studying $ A / (x + B) + C / (x + D) $
without derivatives . . . . . . . . . . 319--321
Paul Stephenson Pappus in two dimensions, Mamikon in
three . . . . . . . . . . . . . . . . . 322--325
Nick Lord An area conundrum . . . . . . . . . . . 325--327
Paul Stephenson Trigonometric identities from regular
polygons . . . . . . . . . . . . . . . . 327--334
Martin Perkins and
David Hopkins Correspondence . . . . . . . . . . . . . 335--336
Anonymous Feedback . . . . . . . . . . . . . . . . 337--338
N. J. L. Problem Corner . . . . . . . . . . . . . 339--343
Stan Dolan Student Problems . . . . . . . . . . . . 344--347
Martin Griffiths Book Review: \booktitleNumber treasury
3: investigations, facts and conjectures
about more than 100 number families (3rd
edn.), by Kenney, Margaret J. and
Bezuszka, Stanley J., pp. 312, \pounds
25.00 (paper), ISBN 9789814603690, World
Scientific Publishing (2015) . . . . . . 348--349
Peter Hall Book Review: \booktitleDoes mathematical
study develop logical thinking?, by
Inglis, Matthew and Attridge, Nina, pp.
185, \pounds 68 (hard), ISBN
978-1-78634-068-9, World Scientific
(2017) . . . . . . . . . . . . . . . . . 349--349
Ray Huntley Book Review: \booktitleCurricular
resources for classroom use: the case of
mathematics, by Stylianides, Gabriel J.,
pp. 176, \pounds 55.00 (hard), ISBN
978-0-19874-989-9, Oxford University
Press (2016) . . . . . . . . . . . . . . 350--350
Peter Hall Book Review: \booktitleHigher and
foundation GCSE mathematics revision
cards, by Ledwick, Mary, each 90 cards,
Higher \pounds 7.99, Foundation \pounds
7.49, ISBN 978-0-90658-884-0, The
Mathematical Association (2016) . . . . 350--351
Roger Patterson Book Reviews: \booktitleMathematics HL:
Sets, relations & groups, by Quinn,
Catherine; Blythe, Peter; Sangwin,
Chris; Haese, Robert and Haese, Michael
pp. 176, AU\$41.00 (paper), ISBN
978-1-92197-232-4, Haese Mathematics
(2013). \booktitle{Mathematics HL:
Calculus}, by Quinn, Catherine; Blythe,
Peter; Sangwin, Chris; Haese, Robert and
Haese Michael, pp. 216, AU\$41.00
(paper), ISBN 978-1-92197-233-1, Haese
Mathematics (2013).
\booktitleMathematics HL: Linear algebra
& geometry, by Quinn, Catherine; Blythe,
Peter; Sangwin, Chris; Haese Robert and
Haese Michael, pp. 344, AU\$54.50
(paper), ISBN 978-1-92197-235-5, Haese
Mathematics (2013).
\booktitle{Mathematics HL: Discrete
mathematics}, by Quinn, Catherine;
Blythe, Peter; Sangwin, Chris; Haese
Robert and Haese Michael pp. 240,
AU\$41.00 (paper), ISBN
978-1-92197-234-8, Haese Mathematics
(2013). \booktitleMathematics HL:
Statistics & probability, by Quinn,
Catherine; Blythe, Peter; Sangwin,
Chris; Haese, Robert and Haese Michael,
pp 208, AU\$41.00 (paper), ISBN
978-1-92197-231-7, Haese Mathematics
(2013)} . . . . . . . . . . . . . . . . 351--353
Nick Lord Book Review: \booktitleElements of
mathematics: from Euclid to Gödel, by
Stillwell, John, pp. 422, \$39.95, ISBN
978-0-691-17168-5, Princeton University
Press (2016)} . . . . . . . . . . . . . 353--355
Owen Toller Book Review: \booktitleMy search for
Ramanujan, by Ono, Ken and Aczel, Amir
D., pp. 238, \pounds 19.99 (hard), ISBN
978-3-319-25566-8, also available as
e-book, Springer Verlag (2016) . . . . . 355--356
Gerry Leversha Book Review: \booktitleMathematics and
the real world, by Artstein, Zvi, pp.
426, \pounds 25, ISBN 978-1-61614-546-0,
Prometheus Books (2014) . . . . . . . . 356--357
P. N. Ruane Book Review: \booktitleA brief history
of numbers, by Corry, Leo, pp. 309,
\pounds 24.99 (hard), ISBN
978-0-19-870259-7, Oxford University
Press (2015) . . . . . . . . . . . . . . 357--358
John Baylis Book Review: \booktitleMeasure and
integration, by Bercovici, Hari; Brown,
Arlen and Pearcy Carl, pp. 300, \pounds
46.99 (hard), ISBN 978-3-31929-044-7,
also available as e-book, Springer
Verlag (2016) . . . . . . . . . . . . . 358--359
Tony Crilly Book Review: \booktitleSourcebook in the
mathematics of medieval Europe and North
Africa, edited by Katz Victor J.,
Folkerts Menso, Hughes Barnabas, Wagner
Roi, Berggren J. Lennart, pp. 574,
\pounds 70.85 (hard), ISBN
978-0-691-15685-9, Princeton University
Press (2016) . . . . . . . . . . . . . . 359--361
Michael De Villiers Book Review: \booktitleMathematical
knowledge and the interplay of
practices, , by Ferreirós, José, pp. 337,
\pounds 31.00 (hard), ISBN
978-0-691-16751-0, Princeton University
Press (2016) . . . . . . . . . . . . . . 361--362
Gerry Leversha Book Review: \booktitleThe best writing
on mathematics 2015, by Pitici, Mircea
(ed), pp 392, \pounds 18.95, ISBN
978-0-691-16965-2, Princeton (2016) . . 362--363
Peter Shiu Book Review: \booktitleSumming it up:
from one plus one to modern number
theory, by Ash, Avner and Gross, Robert,
pp. 229, US\$27.95} (hard), ISBN
978-0-691-17019-0, Princeton University
Press (2016)} . . . . . . . . . . . . . 363--365
Mark Hunacek Book Review: \booktitleMathematical
concepts, by Jost, Jürgen, pp. 312,
\pounds 53.99 (paper), ISBN
978-3-319-20435-2, also available as
e-book, Springer Verlag (2016) . . . . . 365--366
Dominic Yeo Book Review: \booktitleMethods and
techniques for proving inequalities, by
Su, Yong and Xiong, Bin, pp. 222,
\pounds 21.00 (paper), ISBN
978-9-81469-645-6, World Scientific
(2016) . . . . . . . . . . . . . . . . . 366--367
John Baylis Book Review: \booktitleAdvanced calculus
of a single variable, by Geveci, Tunc,
pp. 382, \pounds 37.99 (hard), ISBN
978-3-31927-806-3, also available as
e-book, Springer Verlag (2016) . . . . . 367--368
Mark Hunacek Book Review: \booktitleMatrix groups for
undergraduates (2nd edn.), by Tapp,
Kristopher, pp. 239, \$39.20 (paper),
American Mathematical Society (2016)} 368--369
Mark Hunacek Book Review: \booktitleLie groups, Lie
algebras and representations, by Hall,
Brian C., pp. 354, \pounds 35.99 (hard),
ISBN: 978-1-4419-2313-4, also available
as e-book, Springer Verlag (2015) . . . 369--371
Gerry Leversha Book Review: \booktitlePlain plane
geometry, by Sasane, Amol, pp. 270,
\pounds 40, ISBN 978-9-481474-043-2,
World Scientific (2016) . . . . . . . . 372--373
Gerry Leversha Book Review: \booktitleThe circle;
mathematical exploration beyond the
line, by Posamentier, Alfred S. and
Geretschläger, Robert, pp. 350, \pounds
19.28, ISBN 978-1-63388-167-9,
Prometheus Books (2016) . . . . . . . . 373--375
Owen Toller Book Review: \booktitleBasic discrete
mathematics, by Kohar, Richard, pp. 706,
\pounds 56 (paper), ISBN
978-9-81314-754-6, World Scientific
(2016) . . . . . . . . . . . . . . . . . 375--376
David Bevan Book Review: \booktitleIntroduction to
random graphs, by Frieze, Alan and
Karonski, Michal, pp. 464, \pounds 49.99
(hard), ISBN 978-1-107-11850-8,
Cambridge University Press (2016) . . . 376--377
Gerry Leversha Book Review: \booktitleCatalan numbers,
by Stanley, Richard P., pp. 216, \pounds
29.99, ISBN 978-1-107142774-7, Cambridge
University Press (2015) . . . . . . . . 377--378
John Haigh Book Review: \booktitleClassic topics on
the history of modern mathematical
statistics, by Gorroochurn, Prakash, pp.
754, \pounds 90.50 (hard), ISBN
978-1-119-12792-5, also available as
ebook, John Wiley & Sons (2016) . . . . . 378--379
Dominic Yeo Book Review: \booktitleProblem-solving
challenges for secondary school students
and above, by Linker, David and Sultan,
Alan, pp. 181, \pounds 18.00 (paper),
ISBN 978-9-81473-003-7, World Scientific
(2016) . . . . . . . . . . . . . . . . . 379--380
Peter Giblin Book Review: \booktitleThe population
explosion and other puzzles, by Hess,
Dick, pp. 152, \pounds 23 (paper), ISBN
978-9-814723-375-5, also available as
e-book, World Scientific Press (2016) 380--381
Dominic Yeo Book Review: \booktitle1000 challenges
mathématiques, alg\`ebre, by Aassila,
Mohammed, pp. 643, EUR42.00 (paper),
ISBN 978-2-34001-108-3, Editions
Ellipses (2016). \booktitle1000
challenges mathématiques, analyse by
Aassila Mohammed, pp. 644, EUR42.00
(paper), ISBN 978-2-34001-109-0,
Editions Ellipses (2016) . . . . . . . . 381--382
Peter Hall Book Review: \booktitleStrategy games to
enhance problem-solving ability in
mathematics, by Posamentier, Alfred S.
and Krulik, Stephen, pp. 121, \pounds 20
(paper), ISBN 978-9-81314-634-1, World
Scientific (2017) . . . . . . . . . . . 383--383
Anonymous The Mathematical Association . . . . . . 384--384
Anonymous MAG volume 101 issue 551 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 101 issue 551 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b1
Jennie Golding Is it mathematics or is it school
mathematics?: Presidential address to
The Mathematical Association, April 2017 385--400
Anonymous Looking Back . . . . . . . . . . . . . . 400
Martin Josefsson Further characterisations of tangential
quadrilaterals . . . . . . . . . . . . . 401--411
Stephen Kaczkowski Solving multivariate optimisation
problems using inequalities . . . . . . 412--423
King-Shun Leung Approaching quadratic equations from a
right angle . . . . . . . . . . . . . . 424--438
Martin Bunder and
Joseph Tonien Closed form expressions for two harmonic
continued fractions . . . . . . . . . . 439--448
Stan Dolan Thoughts on a conjecture of Erd\Hos . . 449--457
R. P. Burn Non-Desarguesian planes and weak
associativity . . . . . . . . . . . . . 458--464
Stan Dolan 101.26 Primes of the form $ x^2 + z^2 $ 465
Mowaffaq Hajja 101.27 On the convention that $ {\rm
deg}(0) = - \infty $ . . . . . . . . . . 465--470
Nick Lord 101.28 The versatile exponential
inequality $ e^x \geq 1 + x $ . . . . . 470--475
Kantaphon Kuhapatanakul and
Pongpol Ruankong 101.29 Sums of square roots . . . . . . 476--480
Bill Brading 101.30 A few remarks concerning a class
of infinite sums . . . . . . . . . . . . 480--485
J. A. Scott 101.31 On series for the Euler constant 486--488
J. A. Scott 101.32 Yet another Cantor series . . . . 488--489
Suman Pal and
Baptiste Goujaud 101.33 The application of the
Weierstrass approximation theorem in the
Riemann--Lebesgue lemma . . . . . . . . 489--492
A. F. Beardon 101.34 The area of a quadrilateral . . . 492--494
Jun li 101.35 Some properties of the Kepler
triangle . . . . . . . . . . . . . . . . 494--495
Martin Josefsson 101.36 On the area of a tangential
quadrilateral . . . . . . . . . . . . . 495--497
B. Grivoyannis and
R. Viglione 101.37 Proof Without Words: The birth of
a square (or two) . . . . . . . . . . . 497--498
Martin Josefsson 101.38 Metric relations in crossed
cyclic quadrilaterals . . . . . . . . . 499--502
J. M. Chick 101.39 Another angle on angle? . . . . . 502--508
Paul Stephenson 101.40 Dandelin circles . . . . . . . . 508--511
Marcos Alvarez 101.41 On conics . . . . . . . . . . . . 511--515
J. A. Scott 101.42 The Steiner point revisited . . . 515--516
J. A. Scott 101.43 On the least distance from a
point to a line . . . . . . . . . . . . 517--519
Martin Griffiths 101.44 On a trivariate Fibonacci
identity . . . . . . . . . . . . . . . . 519--522
Bridget M. Torsey 101.45 A note on bounds for the expected
value of a random variable . . . . . . . 522--525
R. V. W. Murphy 101.46 Improved simple pendulum results 525--528
Mowaffaq Hajja and
Edris Rawashdeh 101.47 Notes on Lagrange's interpolation 528--533
Nick Lord The volume of a cone for pre-calculus
students . . . . . . . . . . . . . . . . 534--537
Jonathan Hoseana Extending the substitution method for
integration . . . . . . . . . . . . . . 538--541
Anonymous Feedback . . . . . . . . . . . . . . . . 542--545
Graham T. Q. Hoare Maryam Mirzakhani (1977--2017) . . . . . 545--546
N. J. L. Problem Corner . . . . . . . . . . . . . 547--551
Stan Dolan Student Problems . . . . . . . . . . . . 552--554
Owen Toller Book Review: \booktitleBurn math class
by Jason Wilkes, pp. 416, \$29.99
(paper), ISBN 978-0-46505-373-5, Basic
Books (2016)} . . . . . . . . . . . . . 555--556
Will Hornby Book Review: \booktitleAll is change by
J. F. Riley, pp. 454, \pounds 18 (hard),
ISBN 978-1-909-98664-2, Bookguild
Publishing (2014) . . . . . . . . . . . 556
Peter Giblin Book Review: \booktitleQuite right: the
story of mathematics, measurement and
money by Norman Biggs, pp. 176, \pounds
16.85 (hard), ISBN 978-0-19-875335-3,
Oxford University Press (2016) . . . . . 557--558
Vincent Ting Book Review: \booktitleMath bytes by Tim
Chartier, pp, 136, \pounds 16.95 (hard),
ISBN 978-0-691-16060-3, Princeton
University Press (2014) . . . . . . . . 558--559
Peter Macgregor Book Review: \booktitlePrime numbers,
friends who give problems, a trialogue
with Papa Paulo by Paulo Ribenboim, pp.
320, \pounds 32 (paper), ISBN
978-9-814-72581-1, also available as
e-book, World Scientific, 2016 . . . . . 559--560
Gerry Leversha Book Review: \booktitleCreating
symmetry: the artful mathematics of
wallpaper patterns by Frank A. Farris,
pp. 230, \pounds 24.95, ISBN
978-0-691-16173-0, Princeton University
Press (2015) . . . . . . . . . . . . . . 560--561
Dominic Yeo Book Review: \booktitleThe real analysis
lifesaver by Raffi Grinberg, pp. 193,
\pounds 22.95 (paper), ISBN
978-0-69117-293-4, Princeton University
Press (2017) . . . . . . . . . . . . . . 561--562
John Baylis Book Review: \booktitleTrigonometric
functions and complex numbers by Desheng
Yang, translated by Chunhui Shen, pp.
411, \pounds 32 (paper), ISBN
978-1-93813-486-9, World Scientific
Publishing (2017) . . . . . . . . . . . 562--563
Gerry Leversha Book Review: \booktitleTrigonometry:
notes, problems and exercises by Roger
Delbourgo, pp. 172, \pounds 48, ISBN
978-9-81320-311-2, World Scientific
Publishing (2017) . . . . . . . . . . . 563--565
Michael Fox Book Review: \booktitleTreks into
intuitive geometry: the world of
polygons and polyhedra by Jin Akiyama
and Kiyoko Matsunaga, pp. 425, \pounds
44.99 (hard), ISBN 978-4-431-55841-5,
Springer (2015) . . . . . . . . . . . . 565--568
Peter Shiu Book Review: \booktitleLecture notes on
calculus of variations by Kung Ching
Chang; translated by Tan Zhang, pp. 324,
\$56.00 (paper), ISBN 978-9-81314-623-5,
World Scientific (2017)} . . . . . . . . 568--569
Owen Toller Book Review: \booktitleFinding Fibonacci
by Keith Devlin, pp. 241, \pounds 24.95,
ISBN 978-0-691-17486-0, Princeton
University Press (2017) . . . . . . . . 569--570
Owen Toller Book Review: \booktitleFluke, the math
and myth of coincidence by Joseph Mazur,
pp. 288, \$26.99 (paper), ISBN
978-0-46506-095-5, Basic Books (2016)} 570--571
Peter Giblin Book Review: \booktitleLatin squares and
their applications (2nd edn.), by Donald
Keedwell and Jósef Dénes, pp. 424, \pounds
45.89 (hard), ISBN 978-0-444-63555-6,
North-Holland (2015) . . . . . . . . . . 571--573
John Haigh Book Review: \booktitleStatistics for
mathematicians by Victor M. Panaretos,
pp. 196 (paper), \pounds 35.99, ISBN
978-3-319-28339-5, also available as
e-book, Birkhauser (2016) . . . . . . . 573--574
Anonymous The Mathematical Association . . . . . . 575
Anonymous MAG volume 101 issue 552 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 101 issue 552 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Jessica E. Banks Is a straight line the shortest path? 1--12
Tony Crilly and
Stan Dolan and
Colin R. Fletcher Emmental squares are tasty . . . . . . . 13--22
David L. Farnsworth Axes for symmetric convex curves . . . . 23--30
Alastair Cuthbertson and
Adam McBride and
Doug Stanford A vintage \booktitleListener crossword 31--37
John R. Silvester Variations on a Japanese Temple theorem 38--49
Rory Allen Fisher's $F$-ratio illustrated
graphically . . . . . . . . . . . . . . 50--62
G. J. O. Jameson Fibonacci periods and multiples . . . . 63--76
Matús Harminc and
Lucia Janicková Discrete version of the Pythagorean
theorem . . . . . . . . . . . . . . . . 77--88
Robin T. Clarke 102.01 Hoyle, Bondi and me: a memoir . . 89--93
Stan Dolan 102.02 Minimal sets for congruence
classes . . . . . . . . . . . . . . . . 93--97
Stan Dolan 102.03 When quadratic residues are
squares . . . . . . . . . . . . . . . . 97--100
J. A. Scott 102.04 On the series of Fibonacci
reciprocals . . . . . . . . . . . . . . 100--102
A. F. Beardon 102.05 Remarks on Problem 100.I . . . . 102--104
Joseph Tonien 102.06 A new elementary proof of Euler's
continued fractions . . . . . . . . . . 105--111
Hsuan-Chi Chen 102.07 Evaluating the probability
integral by approximating $ \exp ( -
x^2) $ . . . . . . . . . . . . . . . . . 111--113
Stephen Siklos 102.08 A method of evaluating $ \zeta
(2) $ and $ \int_0^\infty \sin (x) / x
\, d x $ . . . . . . . . . . . . . . . . 114--121
Gareth Williams 102.09 Measurement of polygons and
circles . . . . . . . . . . . . . . . . 121--127
K. B. Subramaniam 102.10 Pythagoras' theorem: a proof by
contradiction . . . . . . . . . . . . . 128
Andrew Jobbings 102.11 Four congruent right triangles 129--131
Yasuo Matsuda 102.12 On circles inscribed in an
ellipse . . . . . . . . . . . . . . . . 131--132
Sava Grozdev and
Hiroshi Okumura and
Deko Dekov 102.13 Distance from the incentre of the
tangential triangle of an obtuse
triangle to the Euler line . . . . . . . 133--135
Sava Grozdev and
Hiroshi Okumura and
Deko Dekov 102.14 A Note on the Feuerbach triangle 135--138
Adrian Chu 102.15 A Faulhaber polynomial by
stacking cubes . . . . . . . . . . . . . 138--140
J. A. Scott 102.16 An areal view of curvature . . . 140--143
Paul Stephenson 102.17 Dimensional analogues of two
figurate identities . . . . . . . . . . 143--146
Lefteris Kirousis and
Georgios Kontogeorgiou 102.18 The probl\`eme des ménages
revisited . . . . . . . . . . . . . . . 147--149
Andrew J. Simoson 102.19 A black hole conundrum . . . . . 150--152
Andrew Jobbings Proofs by folding of the angle sum of a
triangle . . . . . . . . . . . . . . . . 153--154
Nick Lord An unusual inequality challenge . . . . 155--159
Nick Lord Three cameos involving e . . . . . . . . 159--164
C. W. Groetsch Two trajectories: a dynamic monkey tale 164--170
Graham Jameson and
Pauline Jameson Correspondence . . . . . . . . . . . . . 171
Paul Stephenson Feedback . . . . . . . . . . . . . . . . 172--173
N. J. L. Problem Corner . . . . . . . . . . . . . 174--181
Stan Dolan Student Problems . . . . . . . . . . . . 182--184
Owen Toller Book Review: \booktitlePushing limits by
Ted Hill, pp. 224, \pounds 46.50 (hard),
ISBN 978-1-47043-584-4, AMS/Mathematical
Association of America (2017) . . . . . 185
Dave Applebaum Book Review: \booktitleIntroductory
topology, exercises and solutions by
Mohammed Hichem Mortad, pp. 356, \pounds
40, (paper), ISBN 978-9-81314-802-4,
World Scientific (2017) . . . . . . . . 185--186
Donald Keedwell Book Review: \booktitleTaking Sudoku
seriously by Jason Rosenhouse and Louise
Taalman, pp. 214, \pounds 18.49, ISBN
978-0-19-975656-8, Oxford University
Press (2011) . . . . . . . . . . . . . . 186--187
Martin Griffiths Book Review: \booktitleIntroduction to
combinatorics by Gerry Leversha and
Dominic Rowland, pp. 377, \pounds 18
(paper), ISBN 978-1-90600-124-7, United
Kingdom Mathematics Trust (2016) . . . . 187--189
Peter Cameron Book Review: \booktitleErd\Hos--Ko--Rado
theorems: algebraic approaches by
Christopher Godsil and Karen Meagher,
pp. 335 (hard), \pounds 49.99, ISBN
978-1-10712-844-6, Cambridge University
Press (2015) . . . . . . . . . . . . . . 189--190
Graham Hoare Book Review: \booktitleA beginner's
further guide to mathematical logic by
Raymond Smullyan, pp. 277, \pounds 20
(paper), ISBN 978-9-81472-572-9, World
Scientific Publishing (2017) . . . . . . 190--191
David Hopkins Book Review: \booktitleInfinity: a very
short introduction by Ian Stewart, pp.
144, \pounds 7.99 (paper), ISBN
978-0-19-875523-4, Oxford University
Press (2017) . . . . . . . . . . . . . . 191--191
Anonymous The Mathematical Association . . . . . . 192--192
Anonymous MAG volume 102 issue 553 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 102 issue 553 Cover and Back
matter . . . . . . . . . . . . . . . . . b1
Allan J. Kroopnick Linear and non-linear models for
national health expenditures in the USA 193--197
K. Robin McLean Blocks of decimal digits . . . . . . . . 198--202
Stanley R. Huddy and
Michael A. Jones All parabolas through three
non-collinear points . . . . . . . . . . 203--209
Russell A. Gordon Rational arc length . . . . . . . . . . 210--225
Peter Shiu Can our coinage system be improved? . . 226--232
John D. Mahony Tethering in pastures new . . . . . . . 233--245
John D. Mahony From dawn to dusk . . . . . . . . . . . 246--256
Mowaffaq Hajja The existence of triangles, tetrahedra,
and higher-dimensional simplices with
prescribed exradii . . . . . . . . . . . 257--263
Martin Josefsson Metric relations in crossed trapezia . . 264--269
Luis Blanco and
María García-García and
Joaquín Gutíerrez and
Andrea Rios Central force fields and Kepler's laws 270--279
John R. Silvester The seven circles theorem revisited . . 280--301
Anonymous Growing The Gazette . . . . . . . . . . 301
Martin Josefsson The importance of characterisations in
geometry . . . . . . . . . . . . . . . . 302--307
Stephan Berendonk 102.20 The sum of the first $n$ cubes is
a square --- two Proofs without Words 308
Ashvin Rajan 102.21 An addendum to Estermann's proof
of the irrationality of $ \sqrt {2} $ 308--309
Günhan Caglayan 102.22 Proof without Words: sums of sums
of factorials is one less than a
factorial: inductive step . . . . . . . 309--310
Nick Lord 102.23 A visual proof that $ \sqrt {N} $
is irrational . . . . . . . . . . . . . 311--312
Howard Sporn 102.24 Area of a circle via the
Fundamental Theorem of Calculus . . . . 312--314
Nick Lord 102.25 On an alternative formula for the
area of a spherical cap . . . . . . . . 314--316
J. A. Scott 102.26 An ad hoc limiting process . . . 317
J. A. Scott 102.27 On the theorem of means for terms
in AP and GP . . . . . . . . . . . . . . 317--320
G. J. O. Jameson 102.28 A note on series of positive and
negative terms . . . . . . . . . . . . . 320--325
Pedro Ribeiro 102.29 Another proof of the Fundamental
Theorem of Algebra . . . . . . . . . . . 326--328
Michael de Villiers and
Heinz Schumann 102.30 A surprising $3$-D result
involving a hexagon . . . . . . . . . . 328--331
Paul Stephenson 102.31 Cyclic gridpoint polygons . . . . 331--332
Tony Foster 102.32 Panning for gold in the streams
of a regular pentagon . . . . . . . . . 332--335
M. G. Mahmoudi 102.33 A geometrical construction
involving two intersecting circles . . . 335--339
J. A. Scott 102.34 On the vertices of the Kiepert
hyperbola . . . . . . . . . . . . . . . 339--343
Martin Griffiths 102.35 On repetition and divisibility of
parts in partitions . . . . . . . . . . 344--347
Martin Griffiths 102.36 A difference property amongst
certain pairs of Beatty sequences . . . 348--350
Nick Lord Extending runs of composite numbers . . 351--352
Nick Lord Two quick observations about rough
inclined planes . . . . . . . . . . . . 352--353
Anonymous Feedback . . . . . . . . . . . . . . . . 354
N. J. L. Problem Corner . . . . . . . . . . . . . 355--360
Stan Dolan Student Problems . . . . . . . . . . . . 361--363
Peter Giblin Book Review: \booktitleThe story of
calculus by David Acheson, pp. 192,
\pounds 11.99 (hard), ISBN
978-0-19-880454-3, Oxford University
Press (2017) . . . . . . . . . . . . . . 364
Owen Toller Book Review: \booktitleThe joy of
mathematics by Alfred S. Posamentier,
Christian Li, Christian Spreitzer and
Robert Geretschläger, pp. 302, \pounds
15.99 (paper), ISBN 978-1-63388-297-3,
also available as e-book, Prometheus
Books (2017) . . . . . . . . . . . . . . 364--365
Gerry Leversha Book Review: \booktitleThe best writing
on Mathematics 2016 by Mircea Pitici
(ed.), pp. 377, \pounds 27.95, ISBN
978-0-691-17529-4, Princeton University
Press (2017) . . . . . . . . . . . . . . 365--366
Anne Haworth Book Review: \booktitleThe calculus of
happiness by Oscar E. Fernandez, pp.
159, \pounds 19.95 (hard), ISBN
978-0-69116-863-0, Princeton University
Press (2017) . . . . . . . . . . . . . . 367
Martin Griffiths Book Review: \booktitleThe story of
numbers by Asok Kumar Mallik, pp. 196,
\pounds 42.00 (hard), ISBN
978-981-3222-92-2, World Scientific
(2017) . . . . . . . . . . . . . . . . . 367--368
Mark Hunacek Book Review: \booktitleClassical groups,
derangements and primes by Timothy C.
Burness and Michael Giudici, \pounds
50.00, ISBN 978-1-10762-944-8, Cambridge
University Press (2016) . . . . . . . . 368--369
Mark Hunacek Book Review: \booktitleOffice hours with
a geometric group theorist edited by
Matt Clay and Dan Margalit, pp. 441,
\pounds 45.95 (paper), ISBN
978-0-69115-866-2, Princeton University
Press (2017) . . . . . . . . . . . . . . 369--371
David Hopkins Book Review: \booktitleConcise calculus
by Sheng Gong, pp. 674, \pounds 48
(paper), ISBN 978-9-81429-149-1, World
Scientific Publishing Co (2017) . . . . 371--372
Peter Shiu Book Review: \booktitleCalculus in
context: background, basics, and
applications by Alexander J. Hahn, pp.
712, \$70.50 (hard), \pounds 70.50, ISBN
978-1-4214-2230-5, Johns Hopkins
University Press (2017)} . . . . . . . . 372--374
Peter Shiu Book Review: \booktitleA second course
in linear algebra by Stephan Ramon
Garcia and Roger A. Horn, pp. 426,
\pounds 49.99 (hard), ISBN
978-1-107-10381-8, Cambridge University
Press (2017) . . . . . . . . . . . . . . 374--375
Owen Toller Book Review: \booktitleUnsolved! by
Craig P. Bauer, pp. 620, \pounds 27.95
(hard), ISBN 978-0-691-16767-1,
Princeton University Press (2017) . . . 375--376
Martin Griffiths Book Review: \booktitleA walk through
combinatorics (Fourth Edition) by Miklós
Bóna, pp. 593, \pounds 91 (hard), ISBN
978-9-81314-884-0, World Scientific
(2017) . . . . . . . . . . . . . . . . . 376--377
Owen Toller Book Review: \booktitleIntroductory
statistics by Sheldon M. Ross, pp. 828,
\pounds 76 (hard), ISBN
978-0-12804-317-2, also available as
e-book, Academic Press (Elsevir) (2017) 377--378
Ken Zetie Book Review: \booktitleEmmy Noether's
wonderful theorem (revised and updated
edition) by Dwight E. Neuenschwander,
pp. 344, \pounds 22 (paper), ISBN
978-1-42142-267-1, Johns Hopkins
University Press (2017) . . . . . . . . 378--379
A. C. Paseau Book Review: \booktitlePhilosophy of
mathematics by Òystein Linnebo, pp. 203,
\pounds 24.95 (hard), ISBN
978-0-691-16140-2, Princeton University
Press (2017) . . . . . . . . . . . . . . 379--381
Dominic Yeo Book Review: \booktitleMaking and
breaking mathematical sense by Roi
Wanger, pp. 236, \pounds 37.95 (hard),
ISBN 978-0-69117-171-5, Princeton
University Press (2017) . . . . . . . . 381--382
George Tsaknakis Book Review: \booktitleJunior problems
by Andrew Jobbings, pp. 250, \pounds 15.
(paper), ISBN 978-1-90600-130-8, UK
Mathematics Trust (2017) . . . . . . . . 382
Peter Giblin Book Review: \booktitleThe power of
computational thinking by Paul Curzon
and Peter W. McOwan, pp. 220, \pounds 20
(paper), ISBN 978-1-786-34184-6, World
Scientific (2017) . . . . . . . . . . . 382--383
Anonymous The Mathematical Association . . . . . . 384
Anonymous MAG volume 102 issue 554 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 102 issue 554 Cover and Back
matter . . . . . . . . . . . . . . . . . b1
Tom Roper Adventures in shape and space --- and
time . . . . . . . . . . . . . . . . . . 385--400
Meirav Amram and
Miriam Dagan and
Sagi Levi and
Artour Mouftakhov Redundant axioms in teaching linear
algebra . . . . . . . . . . . . . . . . 401--412
King-Shun Leung Paper-folding and cutting activities to
demonstrate five-fold symmetry . . . . . 413--421
Zoltan Retkes Generalising a triangle inequality . . . 422--427
Stephen Kaczkowski On obtaining limiting values of a class
of infinite products . . . . . . . . . . 428--434
R. Michael Range Using high school algebra for a natural
approach to derivatives and continuity 435--446
Anthony F. Constantinides and
George A. Constantinides Spindown Polyhedra . . . . . . . . . . . 447--453
Vincent J. Matsko Lattice dissections: plainer and less
fancy . . . . . . . . . . . . . . . . . 454--459
John R. Silvester On touching circles . . . . . . . . . . 460--470
G. J. O. Jameson Beyond the ratio test . . . . . . . . . 471--484
Tony Gardiner Nature-nurture: finding-feeding . . . . 485--493
Anonymous The \booktitleMathematical Gazette
Information Sheets . . . . . . . . . . . 493
Graham T. Q. Hoare 102.37 Markov numbers . . . . . . . . . 494--496
O. A. S. Karamzadeh 102.38 A very elementary short proof of
Conway's little theorem . . . . . . . . 496--497
B. Sury 102.39 Variants of Carmichael numbers
and Cunningham chains . . . . . . . . . 498--501
P. Stanley 102.40 A nomogram for the solution of
the equation $ p / \sin \theta + q /
\cos \theta = 1 $ . . . . . . . . . . . 501--503
K. B. Subramaniam 102.41 Proof without Words: $ \sin^2 A +
\sin^2 B + \sin^2 C = 4 \sin A \sin B
\sin C $ (where $ A + B + C = \pi $) . . 504
Ángel Plaza 102.42 Proof without Words: An
alternating geometrical series . . . . . 504--505
Ming Fang and
Shahrooz Moosavizadeh and
Mushtaq A. Khan 102.43 A comparative study of relative
rates of change . . . . . . . . . . . . 505--511
Nick Lord 102.44 Another proof of the
irrationality of square roots . . . . . 511--512
G. J. O. Jameson 102.45 Revisiting a note on arithmetic
and geometric means . . . . . . . . . . 513
Hazar Aydin 102.46 Showing the divergence of the
harmonic series using integration . . . 514--515
Dasari Naga Vijay Krishna 102.47 An equilateral triangle
associated with a hexagon . . . . . . . 515--516
Janusz Matkowski and
Alfred Witkowski 102.48 The function $ f(x) / x $ is
v-shaped for convex $f$ . . . . . . . . 517--520
Mowaffaq Hajja 102.49 A very short proof of Pamfilos's
characterisation of the rhombus . . . . 521--523
Saadi Abu-Saymeh and
Mowaffaq Hajja and
Mostafa Hayajneh 102.50 Long altitudes and an unexpected
appearance of the golden ratio . . . . . 523--527
Graham T. Q. Hoare 102.51 Archimedes' quadrature of the
parabola . . . . . . . . . . . . . . . . 527--529
J. A. Scott 102.52 A sum of squares for the Lester
minimum . . . . . . . . . . . . . . . . 529--531
Martin Lukarevski 102.53 The excentral triangle and a
curious application to inequalities . . 531--533
A. F. Beardon 102.54 Unravelling Simpson's paradox . . 534--535
Christian Puritz 102.55 Cable to outer space? . . . . . . 535--537
Nick Lord On the converse of a STEP question about
centroids . . . . . . . . . . . . . . . 538--539
Anonymous In the pipeline for March 2019 . . . . . 539
Anonymous Feedback . . . . . . . . . . . . . . . . 540--542
N. J. L. Problem Corner . . . . . . . . . . . . . 543--550
Stan Dolan Student Problems . . . . . . . . . . . . 551--553
Kevin Davis Book Review: \booktitleSignificant
figures: the lives and work of great
mathematicians by Ian Stewart, pp. 294,
\pounds 21.35 (hard), ISBN
978-0-465-09612-1, also available as
e-book, Basic Books (2017) . . . . . . . 554
Gerry Leversha Book Review: \booktitleA square peg in a
round hole: adventures in the
mathematics of area by Chris Pritchard,
pp. 208, \pounds 17.99, ISBN
978-0-906588-82-6, The Mathematical
Association (2016) . . . . . . . . . . . 554--555
Gerry Leversha Book Review: \booktitleQuestions pupils
ask by Colin Foster, pp. 199, \pounds
15.95 (MA members \pounds 13.45), ISBN
978-0-90658-891-8, The Mathematical
Association (2017) . . . . . . . . . . . 555--557
Dominic Yeo Book Review: \booktitleComing to know:
the introduction of new concepts in
undergraduate mathematics by R. P. Burn,
pp. 114, \pounds 8.59, ISBN
978-0-955-59142-6, MSOR Network
(available via lulu.com) (2009) . . . . 557--558
Peter Macgregor Book Review: \booktitleThe quantum
labyrinth by Paul Halpern, pp. 311,
\$30.00 (hard), ISBN 978-0-46509-758-6,
Basic Books (2017)} . . . . . . . . . . 558
S. C. Coutinho Book Review: \booktitleThe mathematics
of secrets by Joshua Holden, pp. 374,
\pounds 22.95 (hard), ISBN
978-0-691-14175-6, Princeton University
Press (2017) . . . . . . . . . . . . . . 559
Anne Haworth Book Review: \booktitleWeird math by
David Darling and Agnijo Banerjee, pp.
320, \pounds 12.99 (paper), ISBN
978-1-78607-264-1, Basic Books (2018) 560
Owen Toller Book Review: \booktitleClosing the gap
by Vicky Neale, pp. 164, \pounds 19.99
(hard), ISBN 978-0-19878-828-7, Oxford
University Press (2017) . . . . . . . . 561
Dominic Yeo Book Review: \booktitleUndergraduate
convexity, problems and solutions by
Mikkel Slot Nielsena and Victor Ulrich
Rohde, pp. 184, \pounds 32.00 (paper),
ISBN 978-9-81314-364-7, World Scientific
(2017) . . . . . . . . . . . . . . . . . 561--562
Nick Lord Book Review: \booktitleAn introduction
to analysis by Jan Mikusi\'nski & Piotr
Mikusi\'nski, pp. 303, \pounds 73.00
(hard), ISBN 9-789813-2026-10, World
Scientific (2017) . . . . . . . . . . . 562--563
Nick Lord Book Reviews: \booktitleEuler's
pioneering equation by Robin Wilson, pp.
162, \pounds 14.99, ISBN
978-0-19-879492-9, Oxford University
Press (2018). --- \booktitleA most
elegant equation by David Stipp, pp.
221, \$27, ISBN 978-0-465-09377-9, Basic
Books (2017)} . . . . . . . . . . . . . 564--565
Adam McBride Book Review: \booktitleThe calculus
story: a mathematical adventure by David
Acheson, pp. 192, \pounds 11.99 (hard),
ISBN 978-0-19-880454-3, Oxford
University Press (2017) . . . . . . . . 566--567
Owen Toller Book Review: \booktitleTen great ideas
about chance by Persi Diaconis and Brian
Skyrms, pp. 272, \pounds 22.95 (hard),
ISBN 978-0-69117-416-7, Princeton
University Press (2017) . . . . . . . . 567--568
Anne Haworth Book Review: \booktitleMore fallacies,
flaws, and flimflam by Edward J.
Barbeau, \pounds 23.99, ISBN
978-0-88385-580-5, Cambridge University
Press (2017) . . . . . . . . . . . . . . 569
Nick Lord Book Review: \booktitleProofs without
words III by Roger B. Nelsen, pp. 187,
\$50, ISBN 978-0-88585-790-8, MAA Press
(2015)} . . . . . . . . . . . . . . . . 569--570
Mark Hunacek Book Review: \booktitleAn invitation to
applied mathematics by Carmen Chicone,
pp. 856, \pounds 67.15 (hard), ISBN
978-0-128-04153-6, Academic Press
(Elsevir) (2016) . . . . . . . . . . . . 571--572
Anonymous Acknowledgements . . . . . . . . . . . . 573
Gerry Leversha Appeal for referees . . . . . . . . . . 574
Anonymous The Mathematical Association . . . . . . 575
Anonymous MAG volume 102 issue 555 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 102 issue 555 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b2
Sadi Abu-Saymeh and
Mowaffaq Hajja More variations on the Steiner--Lehmus
theme . . . . . . . . . . . . . . . . . 1--11
David Ben-Chaim and
Yechiel Shalitin and
Moshe Stupel Historical mathematical problems
suitable for classroom activities . . . 12--19
Martin Josefsson Area formulas for certain convex
quadrilaterals . . . . . . . . . . . . . 20--27
Daniel Daners and
Theresa Wigmore Conics and a generalised conical
pendulum . . . . . . . . . . . . . . . . 28--40
Leonard M. Wapner The prescient power of indifference . . 41--46
P. Stanley An appraisal of Lalanne's nomogram . . . 47--51
Danilo R. Diedrichs Archimedean, Logarithmic and Euler
spirals --- intriguing and ubiquitous
patterns in nature . . . . . . . . . . . 52--64
Terence Coelho and
Bahman Kalantari How many real attractive fixed points
can a polynomial have? . . . . . . . . . 65--76
W. J. A. Colman Borel's normal number theorem . . . . . 77--86
Emrys Read On the equation $ x^2 + r y^2 = z^2 $ 87--93
Nigel Derby The continued search for sums of powers 94--100
Ken Surendran and
Desarazu Krishna Babu Expressions for rational approximations
to square roots of integers using Pell's
equation . . . . . . . . . . . . . . . . 101--110
Athina Lorentziadi Calculation of $ \pi $ with a needle . . 111--116
Peter Shiu The whole can be very much less than the
sum of its parts . . . . . . . . . . . . 117--127
John D. Mahony ``DIYMathematics'' v. ``ThePackage'' . . 128--129
Joseph Tonien 103.01 New Year identities for 2019 . . 130
Günhan Caglayan 103.02 Proofs without words: identities
in triangular numbers . . . . . . . . . 131--132
Stanley R. Huddy and
Michael A. Jones 103.03 Quotients of hypotenuses of
Pythagorean triples $ (a, b, b + 1) $
and finite differences . . . . . . . . . 132--135
K. Robin McLean 103.04 Does Euclid's construction miss
infinitely many primes? . . . . . . . . 135--137
Samuel G. Moreno and
Esther M. García-Caballero 103.05 Sums of integers . . . . . . . . 137--138
Peter R. Mercer 103.06 Another approach to $ \int_0^\pi
\log (2 \sin u) d u $ . . . . . . . . . 138--140
Peter Shiu 103.07 More on slowly convergent, or
divergent, series . . . . . . . . . . . 140--142
Pedro Ribeiro 103.08 Another classic Fourier analysis
proof of the Basel Problem . . . . . . . 142--145
Martin Josefsson 103.09 On the heights of a convex
quadrilateral . . . . . . . . . . . . . 145--150
J. A. Scott 103.10 Around the nine-point circle . . 150--152
J. A. Scott 103.11 On the Spieker centre of a
scalene triangle . . . . . . . . . . . . 153--154
Peter Giblin 103.12 A note on Problem 101.F . . . . . 154--155
Mieczyslaw Szyszkowicz 103.13 Squaring the circle by using
proportion . . . . . . . . . . . . . . . 156--158
Paul Belcher 103.14 The Party Hat Paradox . . . . . . 159--162
Nick Lord Separating the effects of air resistance
and restitution . . . . . . . . . . . . 163--165
Owen Toller Partial fractions and telescoping series 165--167
Nick Lord More equal volumes of revolution . . . . 168--169
Ian Stewart Correspondence . . . . . . . . . . . . . 170
Anonymous Feedback . . . . . . . . . . . . . . . . 171
Anonymous In the pipeline for July 2019 . . . . . 171
N. J. L. Problem Corner . . . . . . . . . . . . . 172--178
Stan Dolan Student Problems . . . . . . . . . . . . 179--181
Owen Toller Book Review: \booktitleTowards higher
mathematics, a companion by Richard
Earl, pp. 527, \pounds 29.99 (paper),
ISBN 978-1-31661-483-9, Cambridge
University Press (2018) . . . . . . . . 182--183
Adrian Hemery Book Review: \booktitleHow to bake Pi
(previously published as
\booktitleCakes, custard and category
theory) by Eugenia Cheng, pp. 291,
\pounds 9.99 (paper), ISBN
978-1-781-25288-8, Profile Books (2016) 183--184
Peter Giblin Book Review: \booktitleWonders beyond
numbers: a brief history of all things
mathematical by Johnny Ball, pp. 480,
\pounds 16.99 (hard), ISBN
978-1-4729-3999-9, Bloomsbury Sigma
(2017) . . . . . . . . . . . . . . . . . 184--185
Ken Zetie Book Review: \booktitleQ is for quantum
by Terry Rudolph, pp. 164, \pounds 9.95
(paper), ISBN 978-0-99906-350-7,
Terrence Rudolph (2017) . . . . . . . . 185--186
Owen Toller Book Review: \booktitleMusic by the
numbers by Eli Maor, pp. 185, \pounds
19.95 (hard), ISBN 978-0-69117-690-1,
Princeton University Press (2018) . . . 186--187
Gerry Leversha Book Review: \booktitleA common family
weakness for statistics by Chris
Pritchard, pp. 127, \pounds 9.00, ISBN
978-1-911616-03-0, The Mathematical
Association (2018) . . . . . . . . . . . 188--189
Graham Hoare Book Review: \booktitleThe art of logic
in an illogical world by Eugenia Cheng,
pp. 305, \pounds 14.99 (hard), ISBN
978-1-5416-7248-2, Basic Books (2018) 189--190
John Baylis Book Review: \booktitleProfessor
Higgins's problem collection by Peter
Higgins, pp. 126, \pounds 14.99 (paper),
ISBN 978-0-19875-547-0, Oxford
University Press (2017) . . . . . . . . 190
Anonymous MAG volume 103 issue 556 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f3
Anonymous MAG volume 103 issue 556 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b2
Geoffrey Howson Sir Michael Francis Atiyah, O.M., 22
April 1929--11 January 2019 . . . . . . 193--195
John D. Mahony Locating parameters of interest in a
conic section . . . . . . . . . . . . . 196--203
Moshe Stupel and
Avi Sigler and
Jay Jahangiri Teaching proofs without words using
dynamic geometry . . . . . . . . . . . . 204--211
Robert L. Lamphere A hyperbolic proportionality theorem and
hyperbolic surveying problems . . . . . 212--221
David Fraivert New points that belong to the nine-point
circle . . . . . . . . . . . . . . . . . 222--232
David Fraivert Pascal-points quadrilaterals inscribed
in a cyclic quadrilateral . . . . . . . 233--239
John Wiorkowski Finding the probability of a rare real
world event . . . . . . . . . . . . . . 240--247
Christopher D. Hollings The need for closure . . . . . . . . . . 248--256
Bethany Fralick and
Reginald Koo Linear differential equations with
constant coefficients . . . . . . . . . 257--264
Anonymous In the pipeline for November 2019 . . . 264
K. Robin McLean Latin square matrices and their inverses 265--276
Robert Kantrowitz and
Michael M. Neumann Launching a projectile to cover maximal
area . . . . . . . . . . . . . . . . . . 277--284
Leonard van Wyk Rounding versus truncation estimates in
difference calculations . . . . . . . . 285--292
A. F. Beardon The three Steiner--Lehmus theorems . . . 293--304
Paul Stephenson 103.15 When is the sum of the first $n$
consecutive odd cubes a square? . . . . 305--306
Russell A. Gordon 103.16 Variations on a theme . . . . . . 306--312
J. A. Scott 103.17 An unexpected closed form
revisited . . . . . . . . . . . . . . . 312--313
David Gau 103.18 Trigonometric addition and
subtraction formulas, a unified visual
approach . . . . . . . . . . . . . . . . 314--315
Horia V\^\ij\^\iitu 103.19 Bernoulli's inequality for
negative exponents . . . . . . . . . . . 316--317
Russell A. Gordon 103.20 Geometric problems leading to
power means . . . . . . . . . . . . . . 318--323
Paul Levrie 103.21 Closed form evaluation of a class
of improper integrals . . . . . . . . . 323--328
Mowaffaq Hajja 103.22 On a problem of Sastry and a
theorem of Serenus . . . . . . . . . . . 328--332
Martin Josefsson 103.23 On Pitot's theorem . . . . . . . 333--337
Shane Chern and
Shiqiu Qiu 103.24 Partitions, geometric
progressions and a Putnam problem . . . 337--343
Raymond Viglione 103.25 An extension of Thébault's second
problem . . . . . . . . . . . . . . . . 343--346
Emrah Kiliç and
Talha Arikan 103.26 A proof of Clarke's conjecture 346--352
Martin Griffiths 103.27 A property of a particular
unit-distance graph . . . . . . . . . . 353--356
Frank A. Greco How is the scalar product derived? . . . 357--358
Nick Lord Problem Corner . . . . . . . . . . . . . 359--364
Stan Dolan Student Problems . . . . . . . . . . . . 365--367
Ian Anderson Book Review: \booktitleThe beauty of
numbers in nature by Ian Stewart, pp.
224, \pounds 14.99 (paper), ISBN
978-1-78240-471-2, Ivy Press (2017) . . 368
Owen Toller Book Review: \booktitleDiscovering group
theory by Tony Barnard and Hugh Neill,
pp. 219, \pounds 31.99 (paper), ISBN
978-1-13803-016-9, CRC Press (2017) . . 368--369
John Baylis Book Review: \booktitleAn introduction
to analysis by Robert C. Gunning, pp.
370, \pounds 58 (hard), ISBN
978-0-69117-879-0, Princeton University
Press (2018) . . . . . . . . . . . . . . 369--370
S. Collier Coutinho Book Review: \booktitleOrdinary
differential equations, principles and
applications by A. K. Nandakumaran, P.
S. Datti and Raju K. George, \pounds
59.99, ISBN 978-1-10841-641-2, Cambridge
University Press (2017) . . . . . . . . 370--371
Peter Shiu Book Review: \booktitleReal analysis and
applications by Fabio Silva Botelho, pp.
567, \pounds 44.99 (hard), ISBN
978-3-31978-630-8, Springer Verlag
(2018) . . . . . . . . . . . . . . . . . 371--372
Mark Hunacek Book Review: \booktitleThe calculus
gallery by William Dunham, pp. 236,
\pounds 14.99 (paper), ISBN
978-0-69118-285-8, Princeton University
Press (2018) . . . . . . . . . . . . . . 372--374
David Hopkins Book Review: \booktitleConnections in
discrete mathematics: a celebration of
the work of Ron Graham edited by Steve
Butler, Joshua Cooper and Glenn
Hurlbert, pp. 352, \pounds 44.99
(paperback), ISBN 978-1-316-60788-6,
Cambridge University Press (2018) . . . 374--375
Dominic Rowland Book Review: \booktitleCombinatorics: a
very short introduction by Robin Wilson,
pp. 150, \pounds 7.99 (paper), ISBN
978-0-19872-349-3, Oxford University
Press (2016) . . . . . . . . . . . . . . 375--376
Owen Toller Book Review: \booktitleThe model thinker
by Scott E. Page, pp. 410, \$19.99
(paper), ISBN 978-0-465-09463-9, also
available as e-book, Basic Books (2018)} 376
Peter MacGregor Book Review: \booktitleApplied
Mathematics, a very short introduction
by Alain Goriely, pp. 141, \pounds 7.99
(paper), ISBN 978-0-19875-404-6, Oxford
University Press (2018) . . . . . . . . 376--377
Owen Toller Book Review: \booktitleTeaching
statistics by Darren Macey and Will
Hornby, pp. 190, \pounds 19.95 (paper),
ISBN 978-1-10840-630-7, Cambridge
University Press (2018) . . . . . . . . 377--378
Michael Jacoby Book Review: \booktitleSpecial
relativity and classical field theory by
Leonard Susskind and Art Friedman, pp.
448, \$30.00 (paper), ISBN
978-0-46509-334-2, Basic Books (2017)} 378--379
Mark Hunacek Book Review: \booktitleMathematical
physics with partial differential
equations by James Kirkwood, pp. 478,
\pounds 61.99 (paper), ISBN
978-0-12814-759-7, Academic Press (2018) 379--381
Peter Hall Book Review: \booktitleExploring
mathematics: problem-solving and proof
by Daniel Greiser, pp. 320 (paper),
\pounds 29.99, ISBN 978-3-319-90319-4,
Springer Verlag (2018) . . . . . . . . . 381
Tim Morland Book Review: \booktitleIntermediate
problems by Andrew Jobbings, pp. 279,
\pounds 16 (paper), ISBN
978-1-90600-129-2, UK Mathematics Trust
(2018) . . . . . . . . . . . . . . . . . 382
Joel Haddley Book Review: \booktitleVisualizing
mathematics with $3$D printing by Henry
Segerman, pp. 186, \$70 (hard), ISBN
978-1-421-42035-6, Johns Hopkins
University Press (2016)} . . . . . . . . 382--383
Anonymous MAG volume 103 issue 557 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 103 issue 557 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b3
Irene Ault Margaret E. Rayner 21st August
1929--31st May 2019 . . . . . . . . . . 385--387
Paul Glaister Alice's adventures in inverse tan land
--- mathematical argument, language and
proof . . . . . . . . . . . . . . . . . 388--400
Sadi Abu-Saymeh and
Mowaffaq Hajja New proofs of certain characterisations
of cyclic circumscriptible
quadrilaterals . . . . . . . . . . . . . 401--408
Ulrich Abel Coincidence of the barycentre and the
geometric centre of weighted points . . 409--415
Steven J. Kilner and
David L. Farnsworth Characterisations of the parabola . . . 416--430
Curtis Cooper The Chinese Ring puzzle, the Crazy
Elephant Dance puzzle, the $b$-Spinout
puzzle, and Gray codes . . . . . . . . . 431--441
Andrew J. Simoson The morphology of $ \mathbb {Z} \sqrt
{[10]} $ . . . . . . . . . . . . . . . . 442--460
Anonymous In the pipeline for March 2020 . . . . . 460
Stan Dolan A diagram for inequalities of symmetric
functions . . . . . . . . . . . . . . . 461--470
Martin Josefsson Eight formulae for the area of triangle
OIH . . . . . . . . . . . . . . . . . . 471--479
Hans Humenberger and
Franz Embacher Iterating circum-medial triangles . . . 480--487
Gerry Leversha An Appreciation . . . . . . . . . . . . 488
K. B. Subramaniam 103.28 On a link between Triangular and
Fibonacci numbers . . . . . . . . . . . 489--489
Stan Dolan 103.29 Heronian triangles and squares in
arithmetic progression . . . . . . . . . 490--493
Mehdi Hassani 103.30 Tests for divisibility by prime
numbers . . . . . . . . . . . . . . . . 494--495
Peter Shiu 103.31 Factorising numbers with oracles 495--499
G. J. O. Jameson 103.32 More on the gaps between sums of
two squares . . . . . . . . . . . . . . 499--503
Purwanto 103.33 Conditions for the terms of an
arithmetic sequence to form a
multiplicative modular group . . . . . . 504--508
Carlo Del Noce 103.34 Indefinite integration by parts
as a translation of functions . . . . . 508--512
K. Razminia 103.35 Hölder's inequality revisited . . 512--514
Nick Lord 103.36 Three footnotes to Cartwright's
proof that $ \pi $ is irrational . . . . 514--517
Tamsin Forbes and
Tony Forbes 103.37 A sudoku puzzle with a big
rectangular hole . . . . . . . . . . . . 517
Eoghan Bradley and
Mark McCartney 103.38 Four hundred years of the fractal
coastline of Scotland . . . . . . . . . 518--521
Yongcheng Chen 103.39 A lemma to solve Langley's
problem . . . . . . . . . . . . . . . . 521--524
Aldo Scimone 103.40 Identifying golden and
equilateral triangles that arise from
the golden Arbelos . . . . . . . . . . . 525--531
Francisco Javier González Vieli and
Marion Maillard 103.41 A spatial characterisation of
Pascal limaçons . . . . . . . . . . . . . 531--536
J. A. Scott 103.42 The Feuerbach hyperbola revisited 536--538
Martin Lukarevski 103.43 An inequality arising from the
inarc centres of a triangle . . . . . . 538--541
G. J. O. Jameson 103.44 The denominators of the Bernoulli
numbers . . . . . . . . . . . . . . . . 541--548
Robin Murphy 103.45 Improving elementary numerical
integration using numerical
differentiation . . . . . . . . . . . . 548--556
P. Stanley 103.46 A four-hundred year calendar . . 556--558
N. J. L. Problem Corner . . . . . . . . . . . . . 559--566
Stan Dolan Student Problems . . . . . . . . . . . . 567--569
Andy Ashworth Jones Book Review: \booktitleLeadership to
count on, a guide for heads of
mathematics (2nd edn.) by Robin Bevan,
Paul Metcalf and Chris Pritchard, pp.
144, \pounds 14.00 (paper), ISBN
978-0-906588-97-0, The Mathematical
Association (2018). . . . . . . . . . . 570
Peter Giblin Book Review: \booktitleNever a dull
moment: Hassler Whitney, mathematics
pioneer by Keith Kendig, pp. 385,
\pounds 58.50 (paper), ISBN
978-1-4704-4828-8, MAA Press, American
Mathematical Society (2018) . . . . . . 571
Owen Toller Book Review: \booktitleAll sides to an
oval by Angelo Alessandro Mazzotti, pp.
160, \pounds 27.99 (hard), ISBN
978-3-319-39374-2, also available as
e-book, Springer Verlag (2017) . . . . . 572
Owen Toller Book Review: \booktitleIntroduction to
applied linear algebra by Stephen Boyd
and Lieven Vandenberghe, pp. 463,
\pounds 35.99 (hard), ISBN
978-1-31651-896-0, Cambridge University
Press (2019) . . . . . . . . . . . . . . 573--574
Anonymous Acknowledgements . . . . . . . . . . . . 574
Anonymous MAG volume 103 issue 558 Cover and Front
matter . . . . . . . . . . . . . . . . . f1--f2
Anonymous MAG volume 103 issue 558 Cover and Back
matter . . . . . . . . . . . . . . . . . b1--b4
Roger B. Nelsen and
James E. Schultz The Probability that the ``Sum of the
Rounds'' Equals the ``Round of the Sum'' 390--396