Contents
Editorial		193
A celebration of the Olympiad
IMOs I have known	Adam McBride	196
IMO-OMI : Reflections	Tony Gardiner	198
Olympiad memories	C. J. Bradley	201
Question Three	Vin de Silva	202
Ramsey Theory and the IMO	Ben Green	204
Articles
In search of the lost icosahedra	Guy Inchbald	208
The agony and the ecstasy	Ian Bruce	216
(29/25)×(73/43)×(77/65)×(101/75) is close to pi	P. Goetgheluck	228
Power chords	Barry Lewis	233
On Hilbert's third problem	E. C. Zeeman	241
A disc rolling in a tray	Alan F. Beardon	248
Matter for Debate
History of Mathematics in Mathematics: What is the point of it?	P. C. Fenton	254
Notes 86.26 to 86.59
Diophantine triples	Alan F. Beardon and M. N. Deshpande	258
Division power	Philip Maynard	261
"33102pi is an integer!"	Martin Griffiths	263
More on the sequence of prime numbers	Fernando Castro G.	264
Number theory from a combinatorial point of view	Shinji Tanimoto	266
Proof without words:	Peter Holmes	267
Sums of powers of the terms in any finite arithmetic progression	Martin Griffiths	269
Summing integer cubes using Thébault's array of arithmetic sequences	Thomas Koshy	271
Does smaller spread always mean larger product?	Nick Lord	273
On the inverse of the Hilbert matrix	A. Berman and S. Gueron	274
A comment on the solution of finite-difference equations	Panagiotis T. Krasopoulos	277
Derivatives without limits	Doug French	279
Some comments on Euler's series for	Dan Romik	281
More sums involving the floor function	Martin Griffiths	285
Periodically modified power series	S. Simons	287
From the weighted mean to the mean-inequalities	Gyula Darvasi	290
Proof without words: A geometric inequality	Yukio Kobayashi	293
Generalisation of the arithmetic mean - geometric mean - harmonic mean inequality	Zbigniew Urmanin	293
A trigonometrical howler explored	Nick Lord	296
Two proofs of a trigonometric identity	Masakazu Nihei	298
Limits of square roots	Masakazu Nihei	299
Inscribed circles of Pythagorean triangles	Hj. Mohammad Shakil Akhtar	302
More on Simson conics and lines	C. J. Bradley	303
Hero triangles	L. E. Ellis	307
Area of a quadrilateral	J. Harries	310
From triangle to hyperbola	G. Leversha and P. Woodruff	311
Extending the Fermat-Torricelli problem	Nguyen Minh Ha	316
A proof of Nickalls' theorem on tangents and foci of a conic	John Rigby	322
Pythagoras' theorem and similar triangles	K. Ramachandra	324
An eight-point circle	J. A. Scott	326
On the least distance from four fixed points	J. A. Scott	328
The mathematics of equal temperament revisited	Jeremy D. King	329
Components of a force (or any vector)	Janet Jagger	331
Oscillation period in a power-law attractive force field	S. Simons	332
Correspondence		335
Problem Corner	Graham Hoare	338
Student Problems	Tim Cross	343
Reviews		347

For further information about The Mathematical Gazette please contact the Editor.

Students up to the age of 19 are invited to send solutions to either of the problems to Tim Cross, 'MG  SPC', ^c/_o KES, Edgbaston Park Road, Birmingham, B15 2UA. Two prizes will be awarded  a first prize of £25, and a second prize of £20 ? to the senders of the most impressive solutions for either problem. It is, therefore, not necessary to submit solutions to both. Solutions should arrive by 20th September 2002. Please give your school year, the name and address of your school or college, and the name of a teacher through whom the award may be made. The names of all successful solvers will be published in the November 2002 edition of The Mathematical Gazette.