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The Mathematical Gazette Nov 2002

Volume 86 Number 507

Editor Gerry Leversha


Contents


Editorial
 
385

Articles
   
Tangent circles P. Stanley 386
From nested Miquel triangles to Miquel distances Michael de Villiers 390
Equiangular polygons Derek Ball 396
A unified construction of conics Michel Bataille 408
Fermat's little theorem - proofs that Fermat might have used Bob Burn 415
Triangular numbers and perfect squares Tom Beldon and
Tony Gardiner
423
Writing a rational number in Egyptian form Astrid BÖnning, Peter Hilton and Jean Pedersen 432
Digit-distance Mastermind David Ginat 437

Matter for Debate
   
What does really mean? Hugh Thurston 443

43rd International Mathematical Olympiad
Geoff Smith 450

Notes 86.60 to 86.84

   
Immediate successors and predecessors of Fibonacci and Lucas numbers Thomas Koshy 457
Generalised Fibonacci Pythagorean triples Thomas Koshy 459
Proving numbers Catalan Edmund Swylan 460
Generalising the Fibonacci sequence J. A. Scott 463
Some new triples of integers and associated triangles M. N. Deshpande 464
The prime factors of K. Robin McLean 466
The twelve days of Christmas Bill Richardson 468
An algebraic identity revisited J. A. Scott 469
A transformation of periodic recurrence relations S. Simons 471
The vector triple product A. F. Beardon 471
The use of hyperbolic cosines in solving cubic polynomials G. C. Holmes 473
Yet another proof that Nick Lord 477
Some properties of the Farey mean David Singmaster 479
More on iterative solutions of Norman Routledge 481
Number of arrangements A. Ghalamfarsa 484
The 'Self Santa' problem Martin Griffiths 487
Maths bite: sides of regular polygons Nick Lord 490
How many tetrahedra?

Atsuhiro Nakamoto and Mamoru Watanabe

491
On the shape of a flexible elastic string suspended between two points S. Simons 498
Tennis and basketball the lazy way Mostafa Ghandehari 501
Oscillation with different damping models Douglas Quadling 502
Probability of flooding Martin J. Marriott 506
Chain reaction G. Jackson 509
Means of means, some mechanical applications Anthony C. Robin 514
A modified approach to motion under gravity in a resistive medium S. Simons 516

Correspondence
 
518

Problem Corner

Graham Hoare

521

Student Problems

Tim Cross

529

Reviews

532

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