Mathematical Gazette
November 2005

Contents
Articles
Mathematics: The greatest subject in the world	Adam McBride	354
Integral solutions of ass and mule problemsr	David Singmaste	365
The general Vieta-Wallis product for	Thomas J. Osler	371
How rare are singular matrices?	Kerry G. Brock	378
An asymptotic formula for powers of binomial coefficients	Jeff D. Farmer and Steven C. Leth	385
Cycles, bicycles, tricycles and more	Barry Lewis	392
Some comments on inverse arithmetic functions	P. G. Brown	403
-dimensional enrichment for Further Mathematicians	Martin Griffiths	409
Making the real projective plane	Claire Irving	417
The aberrancy of plane curves	Russell A. Gordon	424
About tsunamis	Maurice N. Brearley	437
Matter for Debate
On building polynomials	C. J. Sangwin	441
Notes 89.57 to 89.91
Non-existence of Fibonacci and Lucas numbers in amicable pairs of opposite parity	John H. Jaroma and James M. Mitchell	451
Series connected with the Fibonacci series	Ll. G. Chambers	454
A result on Fibonacci numbers	R. M. Welukar and M. N. Deshpande	455
Another representation of Pythagorean triples	Philip Maynard	456
Rapid decimal expansion of rational fractions	P. MacGregor	458
A new look at	Roy Barbara	460
Fitting triangles to a square	P. G. Brown	461
Digital roots of Mersenne primes and even perfect numbers	Thomas Koshy	464
A simple method for finding tangents to polynomial graphs	Charles Strickland-Constable	466
A short remark on difference equations	IstvÁn Szalkai	467
An elementary derivation of Euler's series for the arctangent function	Hwang Chien-Lih	469
The inequality of means using a difference equation	Nick Lord	471
A trigonometric intersection	Douglas Quadling	473
A cotangent inequality for two triangles	J. A. Scott	473
Some relations between arctangent sums and Pell's equations	Hwang Chien-Lih	474
Ratio and root tests	Kandasamy Muthuvel and Jayanthi Ganapathy	477
More on a generalisation of the limit definition of the Euler constant	R. B. Paris	480
Generalising a recurrence relation	Michael A. B. Deakin	482
Measuring with a piece of string—or putting the into catenary	Nick Lord	484
Seeded tournaments—algorithms, simulations and combinatorics	Martin Griffiths	485
Extended peak numbers	Paul Belcher	490
Proof without words: Pappus' generalisation of Pythagoras' theorem	John H. Jaroma	493
A Heron-type formula for the reciprocal area of a triangle	Douglas W. Mitchell	494
Area properties of triangles revisited	Alex Pathan and Tony Collyer	495
On the Lester circle and the Archimedean triangle	J. A. Scott	498
Dissecting a triangle into a rectangle	Andrew Jobbings	501
Yet more on a neglected Pythagorean-like formula	Gyula Darvasi	502
A short projective proof of Lester's theorem	Michael Duff	505
The equation of the plane containing	Arthur Ellis-Davies	507
A characterisation of the parabola	Mikko Stenlund	507
A global measure of curvature	Anthony C. Robin	511
When shall we three meet tangentially?	Mark J. Cooker	514
Iterated sequences of triangles	H. Brian Griffiths	518
A generalised coin-tossing problem	Philip Maynard	522
Obituary
John William Hersee (1930 ˜ 2005)	Geoffrey Howson	525
Feedback		529
Correspondence		312
Problem Corner	Nick Lord	534
Student Problems	Tim Cross	543
Reviews		546

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