Mathematical Gazette
March 2006
Contents
Articles
Extensions of a theorem of Van Aubel
John R. Silvester
2
Products of lengths of line segments associated with
elliptical chords
Thomas E. Price
13
Numerical integration - a different approach
Harry V. Smith
21
Sums of squares of edge-lengths of cyclic polygons
John Rigby
25
The distribution of the geometric mean
David A. L. Wilson and Barry
Martin
40
The sprinkler problem ~ a mathematician waters the
lawn
Michael A. Jones and Janet L.
Stonick
50
Hexagons with opposite sides parallel
C. J. Bradley
57
Cassini-like formulas for Jacobsthal and Koshy
polynomials
Thomas Koshy and Mohammad
Salmassi
68
Calculating exact cycle lengths in the generalised
Dominic Vella and Alfred Vella
70
Notes 90.01 to 90.30
Fibonacci sequence modulo p
Partitioning sets of polygonal numbers
Philip Maynard
77
The number of partitions of a number into distinct
squares
Michael D. Hirschhorn
80
A metric metre
Tony Barnard
88
Maths bite: two uses for an algebraic identity
Nick Lord
88
Interesting finite and infinite products from simple
algebraic identities
Thomas J. Osler
90
No converse to an isomorphism theorem
Bob Burn
93
A variation on Pythagoras' identity
P. Glaister
96
A trigonometrical surprise: Alexander's angles
Nick Lord
97
Generalising Alexander's angles
Elizabeth M. Glaister and Paul
Glaister
99
Could
Jonny Griffiths
103
Anthony C. Robin
107
Generalising a 'trigonometric' identity
J. K. R. Barnett
110
Square-freedom revisited
J. A. Scott
112
Michael D. Hirschhorn
114
Proof with few words: quadratic convergence of the
AGM
Thomas J. Osler
116
A general version of Simons' integral
Anthony Sofo and Rodney Turner 118
be three?
A simple approximation to
perimeters
and polygonal
Evaluating
Stuart Simons
122
Mean value theorem for integrals generalised to
involve two functions
Jingcheng Tong
126
A modification of the Newton-Raphson method
Stuart Simons
128
Four circles and a triangle
Matthew Lee
130
A generalisation of Archimedes' hatbox theorem
A generalisation of Archimedes'
hatbox theorem
132
A strong result on tiling
Roy Barbara
134
Another calculus proof of the location of Fermat's
point
Jingcheng Tong
135
A right triangle inscribed in a similar right triangle
Hiroshi Okumura and Masayuki
Watanabe
138
On the evaluation of
On the Lester circle, a companion and another special J. A. Scott
case
141
Right answer, wrong reason
Richard Kirby
143
On the M25 problem
John B. Reade
144
How many children?
Martin Griffiths
146
Feedback
150
Problem Corner
Nick Lord
159
Student Problems
Tim Cross
167
Reviews
169
Acknowlegements
191