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The Mathematical Gazette Mar 2000

Volume 84 Number 499

Editor Steve Abbott


Contents

Editorial   1
Articles    
One hundred years on Graham T. Q. Hoare 2
Lewis Carroll - mathematician and teacher of children Canon D. B. Eperson 9
Snubbing with and without eta H. Martyn Cundy 14
The Fermat-Torricelli points of n lines Roy Barbara 24
Continued fractions Robert Macmillan 30
A construction of magic cubes Marián Trenkler 36
The factorial function: Stirling's formula David Fowler 42
A simple energy-conserving model Richard Bridges 51
The Hale-Bopp comet explored with A level mathematics H.R. Corbishley 58

Notes 84.01 to 84.28
   
A portrayal of right-angled triangles which generate rectangles with sides in integral ratio I. Grattan-Guinness 66
Circumradius of a cyclic quadrilateral Larry Hoehn 69
A neglected Pythagorean-like formula Larry Hoehn 71
An unexpected reduced cubic equation J. A. Scott 74
Touching hyperspheres D. F. Lawden 75
Comments on note 82.53 - a generalised test for divisibility Andrejs Dunkels 79
A matrix method for a system of linear Diophantine equations A. J. B. Ward 81
On the applcation of Whittaker's theorem J. A. Scott 84
Digital roots and reciprocals of primes Alexander J. Gray 86
Unexpected symmetry in a derived Fibonacci sequence Alexander J. Gray 87
A recurrence relation among Fibonacci sums Alexander J. Gray 89
Some unusual iterations Mark Thornber 90
When the sum equals the Product Leo Kurlandchik and Andrzej Nowicki 91
Never say never: some mistaken identities Mark J. Cooker 94
A curious property of the integer 24 M. H. Eggar 96
What do cycles of a given length generate? Mowaffaq Hajja 97
A game with positive and negative numbers M. H. Eggar 98
An inductive proof of the arithmetic mean-geometric mean inequality Zbigniew Urmanin 101
Weighted mean in a trapezium Larry Hoehn 102
A formula for integrating inverse functions S. Schnell and C. Mendoza 103
Mathematician versus machine P. Glaister 105
On a conjecture of Paul Thompson Tim Jameson 107
Maximal volume of curved folding boxes Kenzi Odani 110
More on a sine product formula Walther Janous and Jeremy King 113
On a limit for prime numbers J. A. Scott 115
SHM and projections P. Glaister 116
Another cautionary chi-squared calculation Nick Lord 119
More on dual Van Aubel generalisations Michael de Villiers 121

Obituary
 
Sir Wilfred Cockcroft Peter Reynolds 123

Correspondence
 
125

Notices
 
127

Problem corner

G. T. Q. Hoare

128

Students problems

Tim Cross

135

Other Journals

Anne C. Baker

139

Book Reviews
 
140

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


Download the March 2000 issue (2.73MB Acrobat file).

Acknowledgement The file containing the March 2000 issue was taken from the MA CD-ROM for ICME 2000 produced by Bill Richardson.