Table Of Content

The Mathematical Gazette Index to Volume 91 Numbers 520 to 522 M 64 2007 www.m-a.org.uk THE MATHEMATICAL ASSOCIATION £1 Index to the Mathematical Gazette Vol. 91 2007 MONTH PAGES March 1-192 July 193 -— 384 November 385 — 576 Editorials Articles Notes Feedback Teaching Notes Problem Corner Student Problems Correspondence Rev 1ews Editors Matter for Debate Editorials PAGES 1, 385 Articles AUTHOR TITLE lan Anderson Euler and combinatorics P. K. Aravind The Hypercubical Dance C. J. Bradley and G. C. Smith Hagge circles and isogonal conjugation Clotilde Luz Clifton-Everest On the Diophantine equation £ = 1 + ! Tony Crilly Interleaving integer sequences Tony Crilly Galton, Cayley, and the land across the river A. E. L. Davis Some plane geometry from a cone Stan Dolan Man versus Computer M. D. Fox and J. R. Goggins Cevian axes and related curves Doug French Simplicity and Surprise in School Mathematics (Presidential Address 2007) Martin Griffiths ‘Catch-up’ numbers Graham Hoare Leonhard Euler (1707-1783) R. T. Leslie A theorem of M. L. Urquhart's and some consequences Gerry Leversha and G. C. Smith Euler and triangle geometry THE MATHEMATICAL GAZETTE AUTHOR TITLE PAGE Paul Levrie and Hilde Missinne Reflections on an exponential mirror Barry Lewis Trigonometry and Fibonacci numbers Nick Lord Intriguing integrals: an Euler-inspired odyssey K. Robin McLean Groups of rational functions R. V. W. Murphy Differential equations David K. Neal Average lengths for the two-player Name Game Mike Pearson and Ian Short Magic letter groups Douglas Quadling Further forays into dimensions Dave L. Renfro The Hindu method for completing the square Peter Shiu Euler's contribution to number theory Correspondence Robert J. Clarke Nick Lord Michael D. Hirschhorn Stuart Simons Matter for Debate AUTHOR TITLI Jim Farmer Misconceptions of randomness and expected sequential pairs in a permutation of integers Feedback March Michael Hirschhorn pp. 153-154 July Alan Beardon Michael Hirschhorn Graham Hoare . 349-356 Nick Lord David Nelson John Silvester — ember ~ David Bevan ~ ALE.L. Davis ~ Mike Hirschhom | pp. 550-560 Graham Hoare Tony Robin onal | L Miscellaneous Twelfth Annual Mathematical Gazette Writing Awards JSTOR and The Mathematical Gazette Acknowledgements INDEX Notes March 91.01 —91.28 July 91.2—9 91.57 November 91.58 -— 91.71 AUTHOR NO rITLt Roy Barbara 91.07 Sums of cubes in finite fields Roy Barbara 9] Fermat's last theorem in the case n Roy Barbara 9] Steiner-Lehmus, revisited Alan F. Beardon 91. Fibonacci meets Chebyshev Alan F. Beardon 91.3 Functional equations and groups Hossein Behforooz Mirror magic squares from Latin Squares Mark Blyth Did Kepler know this? Robin Chapman Square sums of consecutive triangular numbers Robert J. Clarke \ generalisation of Feynman's triangle Gyula Darvasi \ new generalisation of the Pythagorean theorem Prithwijit De and From immersion heaters to buoys Des MacHale Michael de Villiers 9] A question of balance: an application of centroids Michael A. B. Deakin 9 Re-estimating bounds on athletic performance M. N. Deshpande 9] The Pell sequence and Pythagorean triples David Elgin 91. Newton-Raphson revisited Timothy G. Feeman \ geometric characterisation of the power functions and Osvaldo Marrero N. Gauthier Explicit formula for power sums of an arithmetic sequence M. A. Grant The inertia matrix of a uniform solid 1. Grattan-Guinness An elegant arithmetical relationship and its generalisation Martin Griffiths Ball in a bucket Martin Griffiths The highest score in the class Martin Griffiths Pseudo-cony ergents Martin Griffiths Dove-tail sequences Martin Griffiths Deleting blocks of names from a list Michael D. Hirschhorn Extrema of a symmetric function Andrew Jobbings A surprising relationship? Thomas Koshy lhe central elements in Josef's triangle Philip W. Kuchel 91.69 Can you ‘bend’ a truncated octahedron? King-Shun Leung and 91.08 Paper folding fractions Chong-Lap Sze THE MATHEMATICAL GAZETTE AUTHOR TITLE Nick Lord 31 Maths bite: an unusual proof that \ N is irrational Nick Lord .32 Some more irrational thoughts Nick Lord Folding graphs: a rich source of calculus examples Nick Lord 39 Generalising an examination problem on maximisation Nick Lord An amusing sequence of trigonometrical integrals Nick Lord 52 Similarity properties of the Bride’s Chair Nick Lord 3 Maths bite: the ‘perpendicular-parallel’ axes theorem Zhigin Lu An optimal inequality Des MacHale J, Positive solutions of Mordell’s equation Des MacHale .59 Elementary bounds for the nth prime Des MacHale 1. 4 touch of heuristics Douglas W. Mitchell 91.51 Heron triangles with 7B = 2ZA Douglas W. Mitchell 91. Solving cubics by solving triangles Thomas J. Osler 91. Some long telescoping series Thomas J. Osler and 91.20 Finding ¢ (2) from a recursion relation for Jim Zeng Bernoulli numbers Thomas J. Osler and 91.58 An unusual proof that F,, divides F,,,, using Adam Hilburn hyperbolic functions Frédéric Perrier 91. Carnot's theorem in trigonometric disguise Douglas Quadling 9] Integrals — indefinite or misdefined? Anthony C. Robin 9] A furniture removal problem Norman Routledge 91. Equations with roots in geometrical progression José Carlos Santos 91.45 The fundamental theorem of algebra deduced from elementary calculus J. A. Scott 91. On the Lagrange method for constrained critical points J. A. Scott 91. Some properties of ordered triangle cotangents J. A. Scott 91.23 On generalised Feynman sequences J. A. Scott 91.67 Yet another Kiepert point J. A. Scott 91. Bridging parallelograms of equal area Stuart Simons 91.15 Making toast Stuart Simons 91. How might we model a real fulcrum? Stuart Simons 9] Dynamical analysis of a toy Stuart Simons 9] A geometrical recreation or how to avoid your neighbours Stuart Simons 91. Running a divergent numerical algorithm backwards Paul Stephenson 91.29 Diophantine equations and Farey means INDEX AUTHOR rITLt Sean M. Stewart Linearly-resisted trajectories and the over-under theorem J. Trainin An elementary proof of Pick's theorem Gotz Trenkler and On singular 3 x 3 semi-diagonal Latin squares Dietrich Trenklet Mark B. Villarino The probability of a run S. P. Vincent Archimedes revisited: the approximation of a by regular polygon perimeters Xiaoxia Wang and A new proof of a curious identity Yidong Sun Jon Warwick Modelling penalty competitions to decide football matches : y cos k@ Francis Woodhouse The Basel problem and the zeros of } a K} Francis Woodhouse 4) Some integrals involving In (tanf r) Robert M. Young Another simple proof of the theorem of the means Teaching Notes Michael D. Hirschhorn Teaching integration Jeremy D. King Are even numbers more common than odd numbers? Nick Lord Golden bounds for the roots of quadratic equations Des MacHale Vector addition in the 21st century vi THE MATHEMATICAL GAZETTE Reviews AUTHOR TITLE REVIEWER PAGI Edwin A. Abbott Flatland Nick Lord 382 William J. Adams Think first, apply math, think further Dennis Morris — food for thought Sander Bais The equations: icons of knowledge Ken Zetie Cristoforo Sergio Bertuglia Nonlinearity, chaos and complexity: P. N. Ruane and Franco Vaio The dynamics of natural and social systems Richard Bornat Proof and disproof in formal logic: Clive Kilmister an introduction for programmers John P. Burgess Fixing Frege Michael Ward Paul Cull, Mary Flahive Difference equations: from rabbits to chaos Tony Crilly and Robby Robson David C. M. Dickson Insurance risk and ruit N. H. Bingham William Dunham The calculus gallery: Masterpieces Hugh Williams from Newton to Lebesgue P. P. G. Dyke Managing mathematical projects David Hood — with success Michele Emmer (ed) Mathematics and culture II: Visual Gerry Leversha perfection, mathematics and creativity A. C. Fischer-Cripps The mathematics companion Peter MacGregor Torkel Franzen Gédel's theorem — an incomplete guide Clive Kilmister to its use and abuse A. D. Gardiner and Plane Euclidean Geometry Gerry Leversha C. J. Bradley Sam Howison Practical applied mathematics Nick Lord Daniel Huybrechts Complex geometry, an introduction Peter Giblin Rubin H. Landau A First Course in Scientific Computing Peter Shiu Martin Liebeck A concise introduction to pure Michael Ward mathematics (2nd edn) Saunders Mac Lane Saunders Mac Lane: a mathematical Gerry Leversha autobiography Duncan Marsh Applied geometry for computer graphics — Piotr Zarzycki and CAD (2nd edn.) Alberto A. Martinez Negative math Nick Lord John Milnor Dynamics in one complex variable Bill Cox Peter M. Neumann, The collected papers of William Burnside, Des MacHale A. J. S. Mann, Volumes | and 2 Julia C. Tompson (eds) INDEX Vil AUTHOR REVIEWER PAGE Susan Oakes, Alan Pears The book of presidents: 1865 1965 S. C. Russen 570 and Adrian Rice George M. Phillips Mathematics is not a spectator sport Jolin Baylis Yehuda Pinchover and An introduction to partial Derek Stander Jacob Rubenstein differential equations Miles Reid and Geometry and topology P. N. Ruane Balazs Szendroi Karen Saxe Beginning functional analysis James Gazet Elias M. Stein and Real analysis. Measure theory, integration René L. Schilling Rami Shakarchi and Hilbert spaces John Stillwell The four pillars of geometry Mark Hunacek Douglas R. Stinson Cryptography: Theory and practice Peter Shiu 189 (3rd edn) James J. Tattersall Elementary number theory in nine John Baylis 169 chapters (2nd edn) F. R. Watson Elementary mathematics from an Geoff Tennant 569 advanced perspective David Wells Prime numbers, the most mysterious John Baylis figures in math Student Problems Numbers 2006-5 & 6 2007 -1 & 2 2007-3 & 4 2007 -5 & 6 Statement 90 p. 534 91 p. 163 91 p. 366-367 91 p. 566 Solutions 91 pp. 163-164 91 pp £367 369 91 pp. 567-568 Problem Corner Numbers 90 E, F,G,H 90 1,5, K,L Statement 90 p. 354 90 p. 527 Solution 91 pp. 156-162 91 pp. 358-366 Numbers 91 A,B,C, D 91 E, F,G,H 911,J,K,L Statement 91 p. 155-156 91 p. 358 91 p. 561 Solution 91 pp. 561-566 92 92 Vili THE MATHEMATICAL GAZETTE Cover Pictures Image From March Cevian axes and related curves Cevian axes and related curves July ‘Map of Flatland’ The Hypercubical Dance November Euler's tomb The Tercentenary of the birth of Leonhard Euler The 2007 Gazette editorial team Editor Dr Gerry Leversha Production Editor Mr Bill Richardson Reviews Editor Mr Hugh Williams Problem Corner Editor Mr Nick Lord Student Problem Corner Mr Tim Cross Assistant Editor Mr Tom Roper Proofreaders Mr Colin Davis, Mr Michael Fox Dr Andrew Jobbings, Professor Adam McBride Thanks to Richard Kirby for his help in checking this index.