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The Mathematical Gazette Mar 2002

Volume 86 Number 505

Editor Steve Abbott


Contents


Editorial		  
1

Articles		    
Intégrale, longueur, aire G. T. Q. Hoare and N. J. Lord 3
Squares in triangles John E. Wetzel 28
Octagrammum mysticum and the golden cross-ratio Lawrence S. Evans and John F. Rigby 35
Peak numbers Tabitha T.Y. Mingus and Richard Grassl 44
Partitioning a set Barry Lewis 51
Where is the centre of the graph of a polynomial? Ronald Skurnick 59

Notes 86.01 to 86.25		    
A solution for Note 84.35 John E. Cremona 66
Painting by numbers or Polyominoes revisited John R. Silvester 68
Yet another proof of Pythagoras' theorem J. Barry Sutton 72
A dual to a BMO Problem Michael de Villiers 73
Deconstructing a regular (2n + 1)-gon Martin Griffiths 75
Infinite roots of the quadratic equation and tangents to conic sections at infinity Yaakov S. Kupitz and Horst Martini 76
Morley's theorem once again J. A. Scott 80
An areal view of Feuerbach's theorem J. A. Scott 81
Learning some trigonometrical identities by simple figures Fukuzo Suzuki 83
Some constructions for dividing a trapezium into parts of given area Gyula Darvasi 88
When is an oval not an ellipse? Nick Lord 92
Definite integration via areas Anand Kumar 95
A novel inequality S. Simons 99
An infinite series revisited J. A. Scott 101
In praise of the Catalan constant J. A. Scott 102
Two other transcendental numbers obtained by (mis)calculating Nick Lord 103
A digit function with infinitely many 1-cycles D. C. Morrow 105
Infinitely many primes in arithmetic progressions: the cyclotomic polynomial method Shay Gueron and Ran Tessler 110
The attractor property and matrix equations: an empirical approach A. J. B. Ward 114
On a theorem of G. H. Hardy concerning golf G. L. Cohen 120
Approximating on a spreadsheet Phil Colville 125
A third order iterative scheme David Elgin 126
Average bridge points Philip Maynard 128
Random dart averages Philip Maynard 131
Hymne to Hymen Blanche Descartes via C. A. B. Smith 133

Obituary		    
Peter Reynolds Steve Abbott 137
Memories of Peter Reynolds Mike Cornelius 141

Correspondence		  
142

Problem corner
Graham Hoare
146

Student Problems
Tim Cross
152

Reviews
155

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


Student Problems

Problem 2002.1

For each three-digit positive integer N, define f(N) to be the sum of the hundreds digit, the square of the tens digit and the cube of the units digit, of N. Determine, with proof, all such N for which f(N) = N

Problem 2002.2

In triangle ABC, the midpoint of BC is D. Given that angle ADB = 45° and angle ACB = 30°, determine angle BAD.

Students up to the age of 19 are invited to send solutions to either of the problems to Tim Cross, 'MG  SPC', c/o KES, Edgbaston Park Road, Birmingham, B15 2UA. Two prizes will be awarded  a first prize of £25, and a second prize of £20 ? to the senders of the most impressive solutions for either problem. It is, therefore, not necessary to submit solutions to both. Solutions should arrive by 20th May 2002. Please give your school year, the name and address of your school or college, and the name of a teacher through whom the award may be made. The names of all successful solvers will be published in the July 2002 edition of The Mathematical Gazette.

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