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The Mathematical Gazette July 2005

Mathematical Gazette July 2005


mathematical gazette cover july 2005



Contents


Editorial
 
193

Articles
   
Cyclotomic polynomial factors Richard Grassl and
Tabitha T.Y. Mingus
195
Functional equations and groups Malcolm Perella 202
A new algorithm for computing the logarithmic function Stuart Simons and Andrew Tworkowski 212
Timetable spread and lattice energies Jeremy D. King 222

Matter for Debate
   
Should we reform the teaching of calculus? Hugh Thurston 233

Notes 89.28 to 89.56

   
When the perimeter divides the area of a triangle Philip Maynard and Yinghui Zhou 235
An extension of the fundamental theorem on right-angled triangles Dominic Vella and Julia Wolf 237
A short note on the divisibility of numbers consisting of repeated digits Michael Smith 244
Comment on Mersenne composites and cyclotomic primes   Patrick Quill 245
On a particular Diophantine equation Des MacHale 246
Determinants of binomial coefficients K. Robin McLean 247
Proof without words-arc length of the cycloid Thomas J. Osler 250
Another look at the calculus power rules Sidney Schuman 251
On evaluating the probability integral: a simple one-variable proof Robert M. Young 252
Series for Pi derived from the Gregory-Leibniz series Hwang Chien-Lih 254
An identity involving binomial coefficients Michael D. Hirschhorn 256
Yet another look at a curious identity J. A. Scott 259
A difference equation approach to a curious number J. A. Scott 259
The golden ratio--the right triangle-and the arithmetic, geometric, and harmonic means Angelo Di Domenico 261
Donofrio's theorem Raymond N. Greenwell 261
Some convergent real sequences related to Euler's constant Gh. Costovici 262
A curious identity proved by Cauchy's integral formula Helmut Prodinger 266
A binomial identity, via derangements Leo Chao, Paul DesJarlais
and John L. Leonard
268
Extended polygons Philip Maynard 270
The generalised coin weighing problem Michael Wetherfield 275
The twelve coin problem Cedric S 280
A Ceva-type theorem for the cyclic quadrilateral Larry Hoehn 282
On Viviani's theorem in three dimensions Ken-ichiroh Kawasaki,
Yoshihiro Yagi and Katsuya Yanagawa
283
On the tetrahedron inequality Philip Maynard 287
Approximate constructions for regular polygons Martin Perkins 290
Discrete cycloids Philip Maynard and Yinghui Zhou 292
Another decreasing sequence of triangles J. A. Scott 296
Integral Apollonian circle packings and touching sets Paul Stephenson 297
On spiders, cranes, fishing lines, balloons, mines etc. Stuart Simons 301 301
   

Feedback

304

Correspondence
312

Problem Corner

Nick Lord

314

Student Problems

Tim Cross

323

Reviews

326

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