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The Mathematical Gazette Mar 2003

Volume 87 Number 508

Editor Gerry Leversha


Contents


Editorial

1

Articles
   
Tales from the Mathematical Classroom Sue Sanders 3
Cedric Smith - a mathematical castaway Tony Crilly 18
The story of Blanche Descartes

Cedric A. B. Smith and Steve Abbott

23
The number of ways of grading examination candidates W. T. Tutte and Cedric A. B. Smith 34
Heron triangles and touching circles Christopher J. Bradley 36
On Napoleon triangles and propeller theorems Zvonko Èerin 42
A unique property of right-angled triangles Gyula Darvasi

51

Some features of the general Fermat point S. Simons

60

Mersenne composites and cyclotomic primes Jim MacDougall

71

A polynomial that is a statistical prism

Mark J. Osborne and
Michael J. Osborne

76

Diagrams for difficult problems in probability

Peter C.-H. Cheng and Nigel G. Pitt

86


Notes 87.01 to 87.29

   
Sums of squares with digit restrictions V. Tyagi 98
Sums of consecutive positive integers Tom M. Apostol 98
The prime factors of K. Robin McLean 101
When is  a member of a Pythagorean triple? Dominic and Alfred Vella 102
A simple proof of the fundamental theorem of arithmetic  Paolo Starni 106
A theorem on rational numbers Christopher J. Bradley 107
The golden euro Douglas Quadling 111
The dimension of the space of magic squares A. F. Beardon 112
Fermat row-eliminated matrices and some binomial determinants H. Teimoori and M. Bayat 114
On the ratio of the inradius to the circumradius of a triangle Michael S. Longuet-Higgins 119
How do we tackle S. Simons 120
Generalising an integration 'joke' Nick Lord 123
Maths bite: seeing the divergence of the harmonic series Nick Lord 125
Limits of certain sequences Masakazu Nihei 126

Improving the convergence of monotonic series

J. A. Scott 128
On computing the value of   from the series for  -- a novel linearisation procedure S. Simons 129
An unusual product for and variations of Wallis's product Thomas J. Osler 134
A curious identity revisited Robin Chapman 139
A property of additive functions ÁrpÁd BÉnyi 141
The irrationality of , , , A. L. Brown 143
Curious numbers revisited Manfred Ritter 144
Some identities for an old combinatorial sum Michel Bataille 144
Triangles with a 60° angle and sides of integer length Bob Burn 148
Rep-multiple tile sets Paul Stephenson 154
More sequences from polygons Martin Griffiths 157
Some geometrical examples of proof by reductio ad absurdum  J. A. Scott 161
Areal coordinates at the circus J. A. Scott 162
A geometrical key to the solution of the differential equation: Yukio Kobayashi 163
Combining sets of marks David Frost 166

Correspondence
 
169

Problem Corner

Graham Hoare

171

Student Problems

Tim Cross

175

Reviews

178

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