# 1089 and All That: A Journey into Mathematics

Think of a three-figure number such that its first and last digit differ by two or more. Now, reverse the number, and subtract the smaller of the resulting two numbers from the larger: for example, 782 – 287 = 495. Finally, reverse the new three-digit number, and add: 495 + 594 = 1089. Whatever your initial choice, the result is always 1089. This wonderful and rather surprising trick serves as an opening of the lovely book by David Acheson, a professor at Jesus College, Oxford, and a jazz guitar player, according to whom this ‘1089-trick’ had been the first piece of mathematics that had really impressed him when he learnt it back in 1956. The trick even made the title of the book.
This simple algebraic idea is a well-chosen appetiser, giving the reader an idea of what to expect from this nice little book. The author pinpoints, in a witty and reader-friendly style, certain interesting facts from mathematics and related subjects. The book is obviously aimed at an audience far wider than just professional mathematicians, but each reader, whether mathematician or keen layman, will be delighted. David Acheson writes in his own style, the main feature of which is the fascinating fact of how much he is able to communicate in a rather small amount of words. Naturally, he has something to say about many of the notorious and often publicised pieces from mathematics, history, applications and, of course, famous open problems (or famous ex-open problems that had been open for a long time and have been solved recently). Well-known topics are not missing in the book, but even though typical readers will have at least some knowledge of all these, they will always find something new and interesting in this book.
Several chapters of the book are outstanding and deserve extra mention here. First, from the past, is mathematical analysis (calculus) with its great explanation of the Leibniz dy/dt notation, and one of the subsequent chapters in which the origin of the leopard’s spots is claimed to be governed by a certain differential equation. Another is the chapter on the magical Indian rope trick [see David Acheson’s article in this issue: ed]: a length of a rope is thrown up in the air and stays there, defying gravity. A small child then climbs the rope. The author obtained a rather sophisticated mathematical description of this remarkable phenomenon and, to demonstrate it, persuaded a friend to construct an upside-down double pendulum. Equipped for both theory and experiment, they then proved that the trick really works. They demonstrated unbelievable stability in the pendulum: after being pushed over by as much as 40 degrees, it would gradually wobble back to the upward vertical.
There are more fascinating things in the book that cannot be described here. So, here is the message to all potential readers of this type of mathematical writing: even though you have doubtless read everything by Keith Devlin, Simon Singh, Martin Gardner, Raymond Smullyan, Lewis Carroll and you-name-it, this wonderful work is yet another ‘must’ for your bookshelf!

Reviewer:
lp
Book details

Published:
2002
ISBN:
0-19-851623-1
Price:
£12.99
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