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
Notes 90.01 to 90.30
Cassini-like formulas for Jacobsthal and Koshy polynomials	Thomas Koshy and Mohammad Salmassi	68
Calculating exact cycle lengths in the generalised Fibonacci sequence modulo p	Dominic Vella and Alfred Vella	70
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 be three?	Jonny Griffiths	103
A simple approximation to and polygonal perimeters	Anthony C. Robin	107
Generalising a 'trigonometric' identity	J. K. R. Barnett	110
Square-freedom revisited	J. A. Scott	112
Evaluating	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
On the evaluation of	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 Lester circle, a companion and another special case	J. A. Scott	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

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