Contents
Editorial		193
Articles
Fibonacci numbers and trigonometry	Barry Lewis	194
The irrationality of : a simple proof	Michael Eastham	205
Cyclotomic and double angle polynomials	K. Robin McLean	208
Creating recreational Hamiltonian cycle problems	Mark A. M. Lynch	215
Triangles in squares	Liping Yuan and Ren Ding	219
A pseudohedron	H. Martyn Cundy	226
Some unusual space-filling solids	P. Gailiunas	230
On the generalised birthday problem	R. J. McGregor and G. P. Shannon	242
Trigonometric identities and functional equations	Pl. Kannappan	249
Notes 88.31 to 88.51
Sum of the factorials of the digits of integers	Shyam Sunder Gupta	258
SFD chains and factorion cycles	Steve Abbott	261
Yet another proof of the infinitude of primes	Neville Robbins	263
A short proof of Aubry's theorem	Roy Barbara	263
The number of terminating zeroes of	Nick Lord	264
They are almost all irrational!	Hwang Chien-lih	266
Congruence relations for traces of matrix powers	Shinji Tanimoto	266
Some observations on the method of arctangents for the calculation of	Hwang Chien-lih	270
A modification to the  limit	Anthony C. Robin	279
When is  real?	Stuart Simons	281
Two more maximum problems without calculus	Finbarr Holland	284
Bounds for arithmetic mean of means	Gian Mario Gianella	286
Remarks on the geometric mean--arithmetic mean inequality	Grzegorz Rz±dkowski	290
On a unified method of solving some inequalities	Isao Asiba and Masakazu Nihei	292
Extending a GCSE coursework task on consecutive sums	Nick Lord	298
Feynman's triangle	R. J. Cook and G. V. Wood	299
An alternative characterisation of the Brocard points	Fukuzo Suzuki	302
Escribed and inscribed circles of Pythagorean triangles	Nic Heideman	305
Is the lemniscate of Bernoulli one of Lissajous' figures?	Charles Strickland-Constable	308
Breaking your washing line--how to minimise the risk	Stuart Simons	311
How lawyers make a living	Anthony C. Robin	313
Feedback		316
Correspondence		322
Problem Corner	Nick Lord	323
Student Problems	Tim Cross	330
Reviews		333

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