Table Of Content

The Mathematical Gazette Index to Volume 89 | Numbers 514 to 516 M 64 2005 THE MATHEMATICAL ASSOCIATION Index to the Mathematical Gazette Vol. 89 MONTH March July November Editorials Articles Notes Feedback Obituary Problem Corner Student Problems Correspondence Reviews Editors Matters for debate Editorials PAGES 1, 193 Articles AUTHOR TITLE Maurice N. Brearley About tsunamis Kerry G. Brock How rare are singular matrices? P. G. Brown Some comments on inverse arithmetic functions Jeff D. Farmer and An asymptotic formula for powers of Steven C. Leth binomial coefficients David Ginat Mathematical operators and ways of reasoning Russell A. Gordon The aberrancy of plane curves Richard Grassl and Cyclotomic polynomial factors Tabitha T.Y. Mingus Martin Griffiths n-dimensional enrichment for Further Mathematicians Claire Irving Making the real projective plane Jeremy D. King Timetable spread and lattice energies Barry Lewis Cycles, bicycles, tricycles and more Adam McBride Mathematics: The greatest subject in the world (2005 Presidential Address) K. Robin McLean Partitions of primes and other sequences THE MATHEMATICAL GAZETTE AUTHOR TITLE PAGE K. Robin McLean The tiling conjecture for equiangular polygons Thomas J. Osler The general Vieta-Wallis product for Malcolm Perella Functional equations and groups Tim S. Roberts The discovery of two new magic knight's tours Stuart Simons and A new algorithm for computing the logarithmic function Andrew Tworkowski David Singmaster Integral solutions of ass and mule problems Tony Ward Difference equations, determinants and the Secret Santa problem Matters for Debate C. J. Sangwin On building polynomials Hugh Thurston Should we reform the teaching of calculus? Readers respond Correspondence Martin Griffiths 112 Tony Robin C. M. Jones 312 Alan J. W. Thorn Douglas Quadling 113 Obituary John William Hersee (1930-2005) Geoffrey Howson Feedback March Colin Dixon Michael Hirschhorn Robert Pargeter pp. 104-111 J. A. Scott Doug French Stephen Blair Michael de Villiers Graham Howlett Michael Davies Richard Kirby July Michael Hirschhorn Robert Pargeter Richard Kenderdine pp. 304-311 Timothy Lewis Stan Dolan November Michael Hirschhorn Nick Lord pp. 529-533 Miscellaneous Tenth Annual Mathematical Gazette Writing Awards INDEX Notes March 89.01 — 89.27 July 89.28 — 89.56 November 89.57 — 89.91 AUTHOR NO TITLE Roy Barbara 89.04 An extremum for Xxy where Xx and xyz are constant Roy Barbara 89.62 A new look at x” f=1,|jx-y| = 1 A. F. Beardon 89.17 Flexible quadrilaterals Paul Belcher 89.78 Extended peak numbers Ladislav Beran 89.06 Instant unitary matrices P. G. Brown 89.63 Fitting triangles to a square LI. G. Chambers 89.58 Series connected with the Fibonacci series LI. G. Chambers 89.09 The integral | e dx Leo Chao, Paul 89.45 A binomial identity, via derangements DesJarlais and John L. Leonard Hwang Chien-Lih 89.11 Relations between Euler's constant, Riemann's zeta function and Bernoulli numbers Hwang Chien-Lih 89.37 Series for a derived from the Gregory-Leibniz series Hwang Chien-Lih 89.67 An elementary derivation of Euler's series for the arctangent function Hwang Chien-Lih 89.72 Some relations between arctangent sums and Pell's equations r* = pq + | Robert J. Clarke 89.21 Incircles of right-angled triangles Mark J. Cooker 89.89 When shall we three meet tangentially? Gh. Costovici 89.43 Some convergent real sequences related to Euler's constant H. Martyn Cundy 89.23 The lemniscate of Bernoulli Gyula Darvasi 89.18 Converse of a property of right triangles Gyula Darvasi 89.84 Yet more on a neglected Pythagorean-like formula Michael A. B. Deakin 89.75 Generalising a recurrence relation Angelo Di Domenico 89.41 The golden ratio—the right triangle—and the arithmetic, geometric, and harmonic means Michael Duff 89.85 A short projective proof of Lester's theorem THE MATHEMATICAL GAZETTE AUTHOR NO TITLE PAGE Arthur Ellis-Davies 89.86 The equation of the plane 2 containing ABC 50 Emanuel Emanouilidis 89.26 Construction of Pythagorean magic squares Raymond N. Greenwell 89.42 Donofrio's theorem H. Brian Griffiths 89.90 Iterated sequences of triangles Martin Griffiths 02 Some obvious facts about the primes? Martin Griffiths An integral for the careless mathematician Martin Griffiths Convergents to VN via the Farey mean? Martin Griffiths Seeded tournaments algorithms, simulations and combinatorics Michael D. Hirs« An identity involving binomial coefficients Larry Hoehn A Ceva-type theorem for the cyclic quadrilateral John H. Jaroma and Non-existence of Fibonacci and Lucas numbers James M. Mitchell in amicable pairs of opposite parity John H. Jaroma Proof without words: Pappus' generalisation of Pythagoras’ theorem Calculations on face and vertex regular polyhedra Andrew Jobbings Dissecting a triangle into a rectangle Ken-ichiroh Kawasaki On Vivian's theorem in three dimensions Yoshihiro Yagi and Katsuy a Yanagawa thomas Koshy Digital roots of Mersenne primes and even perfect numbers P. T. Krasopoulos \ result on the sequence of primes A moments of inertia proof of Euler's formula for OF Nick I ord Nick Lord The inequality of means using a difference equation Nick Lord Measuring e with a piece of string—or putting the e into catenary P. MacGregor Rapid decimal expansion of rational fractions Des MacHale On a particular Diophantine equation Philip Maynard Perfect, and almost perfect, Pythagorean triangles Philip Maynard When the perimeter divides the area of a triangle and Yinghui Zhou Philip Maynard 89.46 Geometric-mean sequences INDEX AUTHOR NO TITLE Philip Maynard 89.51 Extended polygons Philip Maynard Discrete cycloids and Yinghui Zhou Philip Maynard 89.60 Another representation of Pythagorean triples Philip Maynard 89.9] A generalised coin-tossing problem K. Robin McLean 89.33 Determinants of binomial coefficients John Melville 16 A polygon inequality Douglas W. Mitchell \ Heron-type formula for the reciprocal area of a triangle Kandasamy Muthuvel Ratio and root tests and Jayanthi Ganapathy Michael O'Loughlin A property of rectangles Thomas J. Osler Proof without words—arc length of the cycloid R. B. Paris More on a generalisation of the limit definition of the Euler constant Alex Pathan and Area properties of triangles revisited Tony Collyer Martin Perkins \ pproximate constructions for regular polygons Which is bigger: « Helmut Prodinger \ curious identity proved by Cauchy's integral formula Douglas Quadling A trigonometric intersection Patrick Quill Comment on Mersenne composites and cyclotomic primes Manfred Ritter The crossed ladder problem Anthony C. Robin \ global measure of curvature Norman Routledge More on railway station arches Sidney Schuman Another look at the calculus power rules J. A. Scott Back to the Euler line J. A. Scott Yet more heuristics A. Scott \ nine-point hyperbola A. Scott On the tetrahedron inequality A. Scott 89.39 Yet another look at a curious identity A. Scott 89.40 A difference equation approach to a curious number THE MATHEMATICAL GAZETTE AUTHOR TITLE PAGE J. A. Scott Another decreasing sequence of triangles 296 J. A. Scott 89.71 A cotangent inequality for two triangles 473 J. A. Scott $9.82 On the Lester circle and the Archimedean triangle 498 Stuart Simons 8 What's the quickest route from A to B? 101 Stuart Simons 89.56 On spiders, cranes, fishing lines, balloons, mines etc. 301 Cedric Smith 48 The twelve coin problem 280 Michael Smith A short note on the divisibility of numbers 244 consisting of repeated digits Mikko Stenlund 89.87 A characterisation of the parabola 507 Paul Stephenson 89.55 Integral Apollonian circle packings and touching sets 297 C. Strickland-Constable 89.65 A simple method for finding tangents to polynomial graphs466 Fukuzo Suzuki 89.22 Generalised Lucas circles of a cyclic quadrilateral Istvan Szalkai 8 A short remark on difference equations Hung-Ping Tsao 89.05 Proof without words Dominic Vella, 89.29 An extension of the fundamental theorem Alfred Vella and on right-angled triangles Julia Wolf R. M. Welukar and 89.59 A result on Fibonacci numbers M. N. Deshpande Michael Wetherfield 89.47 The generalised coin weighing problem Robert M. Young 89.36 On evaluating the probability integral: a simple one-variable proof INDEX Reviews AUTHOR TITLE REVIEWER PAGE John A. Adam Mathematics in nature. Modelling Anthony C. Robin 347 patterns in the natural world Martin Aigner and Proofs from THE BOOK (3rd edn.) Gerry Leversha 139 Giinter M. Ziegler Saban Alaca and Introductory algebraic number theory John Baylis Kenneth S. Williams Barbara Allen and Sue Mathematics education: Exploring the Doug French Johnston-Wilder (eds.) culture of learning E. S. Allman & Mathematical models in biology: Nick Lord J. A. Rhodes an introduction Marlow Anderson, Sherlock Holmes in Babylon Gerry Leversha Victor Katz and Robin Wilson (eds.) George E. Andrews and Integer partitions John Baylis Kimmo Eriksson G. Attwood, Core mathematics 1, 2, 3 and 4 Jennie Golding A. Macpherson et al Michéle Audin Geometry Gerry Leversha Ayman Badawi (ed.) Abstract algebra manual Gerry Leversha Keith Ball Strange curves, counting rabbits and A. Robert Pargeter other mathematical explorations O. E. Barndor-Nielsen Kyosi It6: Stochastic processes: Lectures David Applebaum 167 and K-I. Sato, (eds.) given at Aarhus University Albert A. Bartlett The essential exponential Gerry Leversha 136 Marcel Berger A panoramic view of Riemannian geometry Peter Giblin J. L. Berggren Episodes in the mathematics of D. Stander medieval Islam Vasile Berinde Exploring, investigating and discovering Sudan Hansraj in mathematics E. R. Berlekamp, Winning ways for your mathematical plays, J. H. Conway and Volume 3 (2nd edn) Nick Lord R. K. Guy Volume 4 (2nd edn) Nick Lord Jonathan M. Blackledge Digital signal processing Tony Crilly Jonathan M. Borwein Mathematics by experiment. Plausible Graham Hoare and David H. Bailey reasoning in the 21st Century Vill THE MATHEMATICAL GAZETTE AUTHOR TITLE REVIEWER PAGE Nicolas Bourbaki Elements of mathematics. Functions of Patrick Quill 148 a real variable elementary theory Nicolas Bourbaki Integration I (Chapters 1-6) René L. Schilling 565 and II (Chapters 7-9) N. F. Britton Essential mathematical biology Nick Lord R. S. Cantrell and Spatial ecology via reaction-diffusion Bill Cox C. Cosner equations P. M. Cohn Basic algebra Gerry Leversha G. de Barra Measure theory and integration (2nd edn) Tony Crilly Michael D. de Villiers Rethinking proof with The Geometer's 4. J. Oldknow Sketchpad CD-ROM John Derbyshire Prime obsession — Bernhard Riemann John Baylis and the greatest unsolved problem in mathematics Keith Devlin Sets, functions, and logic: an introduction Michael Ward to abstract mathematics (3rd edn) Charles L. Dodgson Euclid and his modern rivals Amirouche Moktefi (Lewis Carroll) Chris Doran and Geometric algebra for physicists Tony Crilly Anthony Lasenby Marcus du Sautoy The music of the primes John Baylis G. Waldo Dunnington Karl Friedrich Gauss: Titan of science 1. Grattan-Guinness: A. W. F. Edwards Cogwheels of the mind: the story Gerry Leversha of Venn diagrams Kimberly Elam Geometry of design Michael de Villiers Rosemary Emanuel Advanced maths: AS core for OCR Gerry Leversha and John Wood Rosemary Emanuel, Advanced maths: A2 core for OCR Gerry Leversha John Wood and Janet Crawshaw Rosemary Emanuel Advanced maths: AS core for EdExcel Gerry Leversha and John Wood Rosemary Emanuel, Advanced maths: A2 core for EdExcel Gerry Leversha John Wood and Janet Crawshaw Rosemary Emanuel Advanced maths: AS core for AQA Gerry Leversha and John Wood