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Magical Mathematics

Magical Mathematics

by Persi Diaconis and Ron Graham; foreword by Martin Gardner
Princeton University Press, Princeton, NJ, 2011
258 pp., illus. 14 b/w, 133 col.  Trade, $29.95; eBook, $29.95

ISBN: 9780691151649; ISBN: 9781400839384.

Reviewed by Phil Dyke
Professor of Applied Mathematics
Plymouth University


I must admit that before I opened this book, I was skeptical.  Here’s yet another book dressing up a popular pastime (magic) in a mathematical cloak in some kind of try at academic respectability.  How wrong I was.  This is a splendid book with lots of wonderful insights.  Quite a lot of it is about cards in one way or another.  Many so-called tricks turn out to be the application of precise mathematics.  Sometimes it is permutations and combinations; at other times it is the more modern mathematics of coding theory that is less than 70 years old.  We learn about de Bruin sequences and about the Gilbreath principle and how this is related to Mandlebrot sets, the famous gingerbread man on multiple scales.  The mathematics is well presented.  If the reader has only poorly remembered school mathematics, then the whole book should still be accessible.  The symbols are restricted to the square root, powers, and indices.  There are numbers, letters to represent numbers, but there is no algebra and certainly no calculus.  Remarkably, the more sophisticated mathematical reader is also hooked; the authors manage the very difficult trick of avoiding condescension yet remaining accessible.   Another feature is analyzing the shuffle in terms of graph theory; perfectly shuffle enough times, and the cards revert to the start position.  This can be represented by a cycle in graph theory.  Modulo arithmetic also comes to the rescue to explain some card tricks and also tricks involving coins and predicting selections.  There are other chapters not about cards.  There’s one on the I Ching and probability, and another particularly interesting one explaining juggling.  Juggling is analysed not in terms of the mechanics of objects but rather by using sequences and modulo arithmetic.  It is this that tells you when to throw and catch, though for potential jugglers the advice on how to throw and what to concentrate on is invaluable and has little to do with mathematics.  Near the end of the book are biographical accounts of interesting people and their particular claims to fame.  Personally I found this very interesting, particularly the piece on Martin Gardner who contributed the preface to this book in what sadly was the year of his death at the advanced age of 95.  I am one of thousands who was led into mathematics as a schoolboy by Martin Gardner’s wonderful books.  Give this book a try; you certainly will not be disappointed.


Last Updated 2 February 2012

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