Volume 88 Number 513

Editor Gerry Leversha

Contents
Editorial		416
Articles
Cyclic quadrilaterals	C. J. Bradley	417
Beyond the Euler summation formula	Barry Lewis	432
Transformed averages	Christian Puritz	441
Generalising Pascal's Triangle	Barry Lewis	447
Henry Briggs: The Trigonometria Britannica	Ian Bruce	457
Watt linkages and quadrilaterals	G. Keady, P. Scales and S. Z. NÉmeth	475
Matter for Debate
What is meant by 'the smallest possible' number?	Gerry Leversha	493
Notes 88.52 to 88.78
Some properties of finite Fibonacci sequences	Dominic Vella and Alfred Vella	494
Comments on 'Triangular numbers and perfect squares'	Michael D. Hirschhorn	500
Thoughts on an optimistic expectation of AbbÉ Mersenne	Peter Hilton and Jean Pedersen	503
Integer roots of cubic equations	Christopher J. Bradley	508
and	Jingcheng Tong	511
A powerful algebraic tool for equiangular polygons	K. Robin McLean	513
On the nature of the eigenvalues of a particular class of matrix	Stuart Simons	514
The 'difference of square roots' function	Jonathan R. Harris	517
An approach to evaluating	S. Simons	519
An inequality by 'rank and file' methods	Finbarr Holland	522
Grandma's identity	Steve Humble	524
A Ramanujan equation	Roderick Forman	525
Convergent Fibonacci-type sequences	Philip Maynard and Yinghui Zhou	529
Algebraic approximations to some transcendentals via an integral	Martin Griffiths	534
The mean-value theorem generalised to involve two parameters	Jingcheng Tong	538
The best bounds to	Chao-Ping Chen and Feng Qi	540
When is the area equal to ?	Mark J. Cooker	542
Two intuitive proofs of Heron's formula	Taichi Maekawa	546
Some impossible constructions in elementary geometry	H. Azad and A. Laradji	548
Aubel's theorem revisited	J. A. Scott	551
The Kiepert centre in areal coordinates	J. A. Scott	553
Which way will it swing?	Stuart Simons	555
General solution for velocity-squared damping	Gerald Newth	556
No consecutive heads	Martin Griffiths	561
Testing for the independence of three events	Glyn George	568
An extended approach to the Julian and the Gregorian calendar	Sohael Babwani	569
Optimal scheduling to minimise waiting time	John S. Croucher	573
Feedback		577
Problem Corner	Nick Lord	588
Student Problems	Tim Cross	593
Reviews		595
Acknowledgements		607

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