Abstract
The advance publicity on the back of the dust jacket includes a commendation by Martin Gardner. In the 1970s I used to await eagerly the arrival of Scientific American, in which Gardner's Mathematical Games column was an unfailing star. This book is of a similar quality and scope.
Gazalé tells us he studied engineering in Egypt, hence the subtitle of the book. He discusses briefly the shape of the Great Pyramid. Its height was originally 280 royal cubits, and its base 440 royal cubits. From this the slope can be found: on these figures it is very close to the arctan of the golden number, 
. Whether this is coincidence or was a design feature is now impossible to tell. There are so many numerical coincidences that given any number, one can find some other number based on a combination of 
, 
, e, etc, which is very close to it. However, from this little diversion we learn that a royal cubit (the Latin cubitum means elbow) was divided into 7 palms, each of which was further divided into 4 fingers. This suggests that the royal finger was rather slender, at 3/4 inch. (Gazalé gives the conversions in an artificial French system of units.)
Iteration is a theme which runs through the book. There is considerable discussion of continued fractions and of iterated roots (e.g. 
) and of iterated tensor products (which he calls Kronecker products). The discussion is enhanced by geometric interpretations, leading to spirals and fractals which are shown in many good figures and a few colour plates.
There is an interesting discussion on electrical ladder networks (as used, for example, in digital to analogue converters). Their connection to continued fractions is useful, and was new to me. The discussion extends to mechanical ladder networks: chains of interconnected pulleys.
In addition to a discussion on the golden number, Gazalé introduces us to another number which he calls a silver number. There appear to be several silver numbers. Manfred Schroeder, in his entertaining book Fractals, Chaos and Power Laws (Freeman, 1991) has a completely different definition of a silver number. I should not be surprised to learn of other `silver' numbers: it does not seem to be a useful sobriquet.
The level of this book is variable: the brief introduction to electric circuit theory, including the difficult concept of the impedance of a transmission line, is rather terse, though this should not present a problem to a physicist. In other places his pace is almost too slow; he devotes a full page to an explicit conversion of 315 to a binary representation.
Some of the material of this book is familiar, but Gazalé's approach is frequently novel, and yields fresh insight. Some of his material is unfamiliar and that yields still further insight.
One minor irritation is that there are a few misprints in the mathematics. Perhaps the publishers should advertise a web site on which corrections to misprints can be shown: perhaps also readers could submit corrections electronically.
I have enjoyed reading (and reviewing) this book. I can wholeheartedly recommend it, both for personal and library purchase.