Contents
Editorial		417
Articles
Taking perspective	Barry Lewis	418
Fibonacci in Hogwarts?	Tomislav Do'liÆ	432
Some properties of repetends	N. J. Armstrong	437
A simple proof of Lester's theorem	John Rigby	444
Morley's diagram generalised	M. D. Fox	453
Balls, boxes and solitary waves	Paul R. Turner	468
Using spreadsheets to divide algebraic expressions	Tony Collyer and Alex Pathan	477
Notes 87.51 to 87.83
A generalisation of Pascal's and Fibonacci's triangle	Zohreh Shishebor	485
On a generalised divisibility property of primes and the Fibonacci numbers	John H. Jaroma	486
But which one is it?	Martin Griffiths	491
Tests for divisibility	R. A. Watson	493
An elementary approach to finding all square-triangular numbers	Jingcheng Tong and Peter A. Braza	494
Conjugates of Pythagorean triples	Jingcheng Tong	496
Using Pythagorean triples to generate square roots of	Douglas W. Mitchell	499
Proof of the theorems of Fermat and Wilson and related results	A. D. Woodall	500
The digital representation ring	Ronald Skurnick	505
On the matrix representation of continued fractions	J. A. Scott	510
Loops of regular -gons	K. Robin McLean and John R. Silvester	512
A pair of floor and ceiling formulas	Thomas Koshy	514
Wrong method but right answer	Anand Kumar	516
Go to work on an egg	G. Corris	516
Can growth be faster than exponential, and just how slow is the logarithm?	John Tolle	522
An equality for certain exponential sums	H. Azad and A. Laradji	525
Sums involving square-free integers	Michael D. Hirschhorn	527
Comment on 85.38 A curious identity	Michael D. Hirschhorn	528
On a precursor to Stirling's formula	Peter R. Mercer	530
A double integral, a rectangular hyperbola and the harmonic mean	J. A. Scott	532
Evaluation of a class of improper integrals of the first kind	Bai-ni Guo and Feng Qi	534
A systematisation of some trigonometric identities	J. K. R. Barnett	539
The number of odd multinomial coefficients	Patrick Quill	545
The new neighbours problem: an algorithmic solution	Michael Robins	546
Some properties of a triangle and a point	Fukuzo Suzuki	548
Two more proofs of Lester's theorem	J. A. Scott	553
A geometrical iteration	S. Simons	557
Steiner-Lehmus revisited	J. A. Scott	561
An inscriptable quadrilateral	Adam Brown	563
On a metric-related function for the triangle	J. A. Scott	565
A connection between Brianchon's theorem and the seven circles theorem	Adam Brown	569
A strange property of floating bodies	Kenzi Odani and Tomoko Murakami	572
The generalised consecutive lottery number problem	Christopher M. Rump	577
Feedback		582
Correspondence		584
Problem Corner	Nick Lord	587
Student Problems	Tim Cross	594
Reviews		597
Acknowledgements		607

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