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No need for leopard skin, just an Indian rope trick

** Review of ***1089 and All That* by David Acheson,

Times Higher Education Supplement, 14 March, 2003
The tone of this little gem of a book is set by the allusion in its
title to the W.C. Sellar and R.J. Yeatman classic
*1066 and All That* and the outrageous Steve Bell
cartoon on its cover. But David Acheson's *Journey into Mathematics* is
never trite or facile.

He starts with a recollection of the magician's
1089 trick (picked up in a children's annual) that gives the book
its title: take any three figure number (457, say), reverse it and subtract
the smaller from the bigger (754-457=297), reverse the result again
and add (297+792=1089). No matter which number the audience
chooses, the magician will be able to predict the result of that little
calculation.
As a small boy, Acheson found this rather more exciting than the
algebra taught at school - not only because his teacher
did not dress up in leopard skin to make algebra more interesting,
as another cartoon in the book suggests.

Acheson sets out to justify algebra by using
it to explain the 1089 trick. From there he takes the reader on a scenic
tour of mathematics, ending with a vista of chaos and catastrophe theory
and a mathematical explanation of the Indian rope trick.
This explanation is based on an original research result of the author that
won him publication in *Nature* and had TV stations queuing
up for interviews.

The book is such an easy and entertaining read (my non-mathematical family
members agree) that one hardly notices how much honest maths the
author manages to convey: quadratic equations, elementary topology,
differential equations, conic sections and so on, each told in its historical
context. And all this in spite of the fact that every other page is taken
up by cartoons or illustrations of all kinds.

There are a few mathematicians who succeed in writing popular
accounts of their craft without being superficial or condescending. With
this little book Acheson has joined the best of them.

H. Geiges