Mathematical Spectrum

Volume 41, Number 1 (September 2008)

1	From the Editor: Thinking Historically
2	AVIV ADLER and ILAN ADLER. Fundamental Transformations of Sudoku Grids
8	JOZEF DOBOŠ. Some Irrationals do not have Special Names
11	JOHN D. MAHONY. Henges, Heel Stones, and Analemmas
21	STUART SIMONS. Circles, Chords, and Difference Equations
23	ROBERT BUONPASTORE and THOMAS J. OSLER. Triangles and Parallelograms of Equal Area in an Ellipse
27	M. A. NYBLOM. Counting the Perfect Powers
32	PRITHWIJIT DE. Curious Properties of the Circumcircle and Incircle of an Equilateral Triangle
36	MICHAEL BEER. Mathematics and Music: Relating Science to Arts?
42	Letters to the Editor: NICK LORD - Regular polygons
43	Problems and Solutions
47	Reviews: Game Theory: A Very Short Introduction, By Ken Binmore

Volume 40, Number 3 (May 2008)

97	From the Editor: People Matter
99	ALEKSANDER MATUSZOK. On Triangular Circles
104	PHILIP MAYNARD. Generalised Binet Formulae
106	THOMAS J. OSLER. Geometric Constructions Approximating ¼
109	P. GLAISTER. One Day Cricket Triangular Tournaments – Do Matches Count?
116	PETER STANLEY. The Better Bowler?
119	ZHANG YUN. Euler's Inequality Revisited
122	PETER MORRIS. A Square Wheel on a Round Track
127	HOSSEIN BEHFOROOZ. On Constructing 4£4 Magic Squares with Pre-Assigned Magic Sum
134	Letters to the Editor: BOB BERTUELLO - Rational approximation to square roots; BOR-YANN CHEN - An extension of extracting a square root; PAUL BELCHER - Circles of best fit; BOB BERTUELLO - Big numbers, happy ending; ALASTAIR SUMMERS - Identical digits
139	Problems and Solutions
143	Reviews: Hesiod's Anvil: Falling and Spinning Through Heaven and Earth, By Andrew J. Simoson

Volume 40, Number 2 (January 2008)

49	From the Editor: Harry Burkill
50	GARETH WILLIAMS. Poincaré and his Infamous Conjecture
56	THEODOROS M. VALAHAS and ANDREAS BOUKAS. The Reflecting Property of Parabolas
59	ABBAS ROOHOL AMINI. Fibonacci Numbers from a Long Division Formula
62	NATHAN OLSON, CHRISTOPHER PHILLIPS and JENNIFER SWITKES. Two Derivations of a Higher-Order Newton-Type Method
67	IAN SHORT. How Much Money do You Need?
73	ANDREW ROBERTSON and THOMAS J. OSLER. Euler's Little Summation Formula and Sums of Powers
77	KALYAAN M. RAO, K. P. S. BHASKARA RAO and M. BHASKARA RAO. The Mathematics Behind a Certain Card Trick
80	Mathematics in the Classroom: ANAND KUMAR. Similar triangles and complex numbers
84	Letters to the Editor: DANIEL SCHULTZ - Regular polygons; BOR-YANN CHEN - Rational approximation to square roots; ALASTAIR SUMMERS - Symmetrical Fibonacci products; CHAN WEI MIN - The power rule for a real exponent
89	Problems and Solutions
92	Reviews: A Garden of Integrals, By Frank Burk; Experimental Number Theory, By Fernando Villegas; The Genius of Euler: Reflections on His Life and Work, Edited by William Dunham; The Early Mathematics of Leonhard Euler, By C. Edward Sandifer; The Magic Numbers of the Professor, By Owen O'Shea and Underwood Dudley; How Euler Did It, By C. Edward Sandifer

Volume 40, Number 1 (September 2007)

1	From the Editor: Problem-Solving, e, and π
3	ZHANG YUN. An Inequality Connected with a Special Point of a Triangle
9	HOSSEIN BEHFOROOZ. On the Divergence of p-like Series with p > 1
17	JOSEPH L. PE. The Picture-Perfect Numbers
24	PHILIP MAYNARD. Sums of Consecutive Numbers Modulo n
26	EDWARD GREVE and THOMAS J. OSLER. Oblique-Angled Diameters and Conic Sections
31	D. G. ROGERS. Picture This: From Inscribed Circle to Pythagorean Proposition
36	Mathematics in the Classroom: M. A. KHAN. Archimedes and parabolic segments
38	Letters to the Editor: ABBAS ROOHOL AMINI - Curious powers; BOR-YANN CHEN - Stability analysis on SARS epidemics; BOR-YANN CHEN - Rational approximation to square roots; M. A. KHAN - Why is 1^3 + 2^3 + · · · + n^3 = (1 + 2 + · · · + n)^2?
41	Problems and Solutions
45	Reviews: Bayes Linear Statistics, By Michael Goldstein and David Wooff; The R Book, By Michael J. Crawley; American Regions Math League & ARML Power Contests 1995–2003, By Donald Barry and Thomas Kilkelly; The Edge of the Universe: Celebrating Ten Years of Math Horizons, Edited by Deanna Haunsperger and Stephen Kennedy

Volume 39, Number 3 (May 2007)

97	From the Editor: It's About Time
99	LYNDON O. BARTON. Construction of a Golden Rectangle with a Given Area
102	A. TAN, R. RAMACHANDRAN and T. X. ZHANG. Cluster Analysis and the Planetary Status of Pluto
109	SHYAM SUNDER GUPTA. Truncatable Semi-Primes
113	DIMITRIS SARDELIS and THEODOROS VALAHAS. The First Indeterminate Diophantine Problem
115	MOHAMED TEYMOUR and THOMAS J. OSLER. The Quadratic Equation as Solved by Persian Mathematicans of the Middle Ages
119	GUIDO LASTERS. Circles of Best Fit
123	J. A. SCOTT. On Sums of Squares of Multivariate Polynomials
126	Mathematics in the Classroom: ELIZABETH M. GLAISTER and PAUL GLAISTER. Forgetting to integrate
127	Letters to the Editor: ALASTAIR SUMMERS - The areas problem; ROBERT J. CLARKE - Symmetrical Fibonacci products; STUART SIMONS - A modified Newton–Raphson procedure; SEBASTIAN HAYES - Square roots by continued fraction convergents
133	Problems and Solutions
137	Reviews: Understanding Uncertainty, By Dennis V. Lindley; Aha! A Two-Volume Collection. Aha! Insight and Aha! Gotcha, By Martin Gardner; The Mathematics of Games and Gambling, By Edward Packel
139	Index

Volume 39, Number 2 (January 2007)

49	From the Editor: The (mis)Behaviour of Markets
51	M. A. KHAN. Rational Approximation to Square Roots of Integers
54	ED RUSSELL and FRAZER JARVIS. Mathematics of Sudoku II
59	KONSTANTINE ZELATOR. Integral Triangles and Diophantine Equations
63	JONATHAN SMITH. 80% Incan
64	STUART SIMONS. A Matrix Inequality with Functional Applications
68	PHILIP MAYNARD. Pythagorean Rectangles
71	THOMAS J. OSLER and JOHN KENNEDY. The Integers of James Booth
73	JOHN C. B. COOPER. The First Class Honours Grade: An Application of the Beta Distribution
75	Mathematics in the Classroom: ANAND KUMAR. Trigonometric substitutions in action
77	Computer Column: PETER MATTSSON. Permutations and combinations or `How I learned to stop worrying and love recursion'
80	Letters to the Editor: BOB BERTUELLO - The rational mean; K. R. S. SASTRY - Brahmagupta's problems, Pythagorean solutions and Heron triangles; ALASTAIR SUMMERS - A special case?; ALASTAIR SUMMERS - Magic squares – a general method
88	Problems and Solutions
92	Reviews: Common Errors in Statistics (and How to Avoid Them), By Phillip I. Good and James W. Hardin; Math Made Visual. Creating Images for Understanding Mathematics, By Claudi Alsina and Roger Nelsen; Visual Statistics: Seeing Data with Dynamic Interactive Graphics, By Forrest W. Young, Pedro M. Valero-Mora and Michael Friendly; 99 Points of Intersection, By Hans Walser (translated from the original German by Peter Hilton and Jean Pedersen)

Volume 39, Number 1 (September 2006)

1	From the Editor: Divisors, maps, and interest
4	SCOTT H. BROWN. The Life and Work of Augustus De Morgan
10	FEI YAO and PAUL BELCHER. Is Anyone Sitting in the Right Place?
15	BERTRAM FELGENHAUER and FRAZER JARVIS. Mathematics of Sudoku I
23	J. GANI. Modelling SARS
27	ATARA SHRIKI. The Areas Problem
31	Mathematics in the Classroom: ANAND KUMAR. Maxima and minima through geometry
35	Letters to the Editor: JENS CARSTENSEN - A geometrical solution to the problem in Mathematical Spectrum, Volume 38, Number 2, pp. 83–84; BOB BERTUELLO - Another solution to the problem in Mathematical Spectrum, Volume 38, Number 2, pp. 83–84; ROBERT J. CLARKE - Gardiner's three circles problem; IAN MCPHERSON - Sudoku possibilities; ALASTAIR SUMMERS - Abundant numbers
40	Problems and Solutions
44	Reviews: Mathematics for Business Decisions: with Interdisciplinary Multimedia Projects, Part 1: Probability and Simulation, By Richard B. Thompson, business projects by Christopher G. Lamoureux and Pamela E. Slaten; USA and International Mathematical Olympiads 2004, Edited by Titu Andreescu, Zuming Feng and Po-Shen Loh; Supporting Assessment in Undergraduate Mathematics, Edited by Lynn Arthur Steen; Case Studies edited by Bonnie Gold, Laurie Hopkins, Dick Jardine and William A. Marion; Mathematical Connections. A Companion for Teachers and Others, By Al Cuoco; When Computers were Human, By David Alan Grier; Index to Mathematical Problems 1975–1979, Edited by Stanley Rabinowitz and Mark Bowron

Volume 38, Number 3 (May 2006)

97	From the Editor: Complexities
99	MICHAL KŘÍŽEK, LIPING LIU and ALENA ŠOLCOVÁ. Fundamental Achievements of Ancient Chinese Mathematicians
108	MATTHEW OSTER and THOMAS J. OSLER. A Spiral of Triangles Related to the Great Pyramid
113	DAVID GROCHOWSKI and THOMAS J. OSLER. An Asymptotic Approach to Constructing the Hyperbola
116	WENJIN HUANG and PAUL BELCHER. The Primitive Pythagorean Magic Forest
120	ALAN HUNTER. Partial Sums of the Harmonic Series Close to an Integer
124	STUART SIMONS. An Approach to Solving Equations with Multiple Modulus Signs
128	PHILIP MAYNARD. Generalizations of the Difference of Two Squares
131	Mathematics in the Classroom: BOR-YANN CHEN. What's in a constant?
132	Letters to the Editor: JONNY GRIFFITHS - Mathematics, with love; ALASTAIR SUMMERS - Extracting cube roots; S. HAYES - Multiples of 11
136	Problems and Solutions
139	Reviews: Reality Conditions. Short Mathematical Fiction, By Alex Kisman; Martin Gardner's Mathematical Games, By Martin Gardner; An Introduction to Statistics Using Resampling Methods and Microsoft Office Excel, By Phillip I. Good; Introduction to Statistics Through Resampling Methods and R/S-PLUS, By Phillip I. Good and Clifford E. Lunneborg; Mathematics in Service to the Community: Concepts and Models for Service-Learning in the Mathematical Sciences, Edited by Charles R. Hadlock; Revise for Core Maths 2, 3 and 4, By Greg Attwood, Alistair Macpherson, Bronwen Moran, Joe Petran, Keith Pledger, Geoff Staley and Dave Wilkins; Understanding Our Quantitative World, By Janet Anderson and Todd Swanson; Real Infinite Series, By Daniel D. Bonar and Michael J. Khoury, Jr

Volume 38, Number 2 (January 2006)

49	From the Editor: How Unique is Factorization?
51	GUIDO LASTERS and DAVID SHARPE. From Squares to Circles by Courtesy of Einstein
56	MICHAL KŘÍŽEK, FLORIAN LUCA and LAWRENCE SOMER. From Fermat Numbers to Geometry
64	P. GLAISTER. Pythagoras — Couched in Mystery?
68	K. R. S. SASTRY. Brahmagupta's Problems, Pythagorean Solutions and Heron Triangles
74	STUART SIMONS. Summing Powers of Roots of an Algebraic Equation
78	ALASTAIR SUMMERS. Equalising Polygons
83	Mathematics in the Classroom: CARSTEN GHEDIA. Finding the length of part of a tangent
85	Letters to the Editor: ALASTAIR SUMMERS - Curious cubes; JOHN MACNAUGHTON - Kepler's polygonial well; JOEL MURANG - An alternative proof for the sum of the first n triangular numbers; M. A. KHAN - Expressing the sum of two cubes as a square; SEYAMACK JAFARI - Right- and left-prime numbers; JOEL MURANG - Thought-provoking tesseracts
89	Problems and Solutions
92	Reviews: Exploring, Investigating and Discovering in Mathematics, By Vasile Berinde; Historical Modules for the Teaching and Learning of Mathematics, Edited by Victor J. Katz and Karen Dee Michalowicz; Musings of the Masters: An Anthology of Mathematical Reflections, Edited by Raymond G. Ayoub; First Lessons for Graphics Calculators, By Alan Graham and Barrie Galpin; The Calculus Gallery. Masterpieces from Newton to Lebesgue, By William Dunham; R. L. Moore: Mathematician & Teacher, By John Parker; Mathematics Elsewhere, By Marcia Ascher; A Concise Oxford Dictionary of Mathematics, Edited By Christopher Clapham and James Nicholson; Advancing Maths for AQA: Statistics 2 & 3, By Roger Williamson and Gill Buque; Advancing Maths for AQA: Core Maths 3, By Greg Atwood, Alistair Macpherson, Bronwen Moran, Joe Petran, Geoff Staley and Dave Wilkins

Volume 38, Number 1 (September 2005)

1	From the Editor: Gauss: Titan of Science
3	THOMAS J. OSLER and JOSEPH DIACO. Ptolemy versus Copernicus
7	JAY L. SCHIFFMAN and CHRISTOPHER S. SIMONS. More Odd Abundant Sequences
9	M. A. NYBLOM. Pick's Theorem and Greatest Common Divisors
12	P. GLAISTER. Equicentric Patterns
17	PHILIP MAYNARD. Partitioning Fibonacci Sets
21	A. TAN, R. RAMACHANDRAN and W. SHENG. Progression of Scores and Averages in Test Cricket
29	LINDA ETTLIN and PAUL BELCHER. But I Only Want to Half Differentiate!
34	Mathematics in the Classroom: JEN-CHIN PANG. Game show problem
36	Letters to the Editor: NORMAN ROUTLEDGE - Fibonacci and Lucas numbers; NICK LORD - Periodic recurrence relations; ALASTAIR SUMMERS - Diophantine equations; JOYCE DAVIES - Square roots by subtraction
40	Problems and Solutions
44	Reviews: Resources for the Study of Real Analysis, By Robert L. Brabenec; Closepacks and Quasi-Closepacks, By Patrick Taylor; Mathematical Delights, By Ross Honsberger; Mathematical Adventures for Students and Amateurs, Edited by David F. Hayes and Tatiana Shubin; Core Mathematics 2, By Greg Atwood, Alistair Macpherson, Bronwen Moran, Joe Petran, Geoff Staley and Dave Wilkins; Advancing Mathematics for AQA: Statistics 1, By Roger Williamson, Gill Buque, Jim Miller and Chris Worth; Advancing Maths for AQA: Mechanics 2, By Ted Graham and Aidan Burrows; Advancing Maths for AQA: Decision Maths 1, By Sam Boardman, Ted Graham, David Pearson and Roger Williamson; Advancing Maths for AQA: Core Maths 1, By Greg Atwood, Alistair Macpherson, Bronwen Moran, Joe Petran, and Dave Wilkins; Advancing Maths for AQA: Core Maths 4, By Greg Atwood, Alistair Macpherson, Bronwen Moran, Joe Petran, Keith Pledger and Dave Wilkins

Volume 37, Number 3 (May 2005)

97	From the Editor: Mathematics, with love
99	PHILIP MAYNARD. Generalizing a Partition Problem
103	P. GLAISTER. When Tweedledum and Tweedledee met Mr Fibonacci
109	JIM ZENG and THOMAS J. OSLER. A Simple Geometric Construction of the Harmonic Mean of n Variables
112	GRAEME COHEN. The Probability of Scoring a Century in Cricket
119	FRAZER JARVIS. Square Roots by Subtraction
123	JOHN C. B. COOPER. The Poisson and Exponential Distributions
126	A. TAN. Estimating the Eccentricity of the Earth's Orbit
130	Mathematics in the Classroom: ANAND KUMAR.