Ask mathematician Midhat J. Gazale, then brace yourself for a heady ride through the wilds of self-similar geometry in Gnomon: From Pharaohs to Fractals, his. Gnomon: From Pharaohs to Fractals by Midhat Gazale and a great selection of related books, art and collectibles available now at Gnomon: from pharaohs to fractals, by Midhat J. Gazalé. Pp. £ ISBN 0 1 (Princeton University Press). – Volume
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Gnomon: From Pharaohs to Fractals
European Journal of PhysicsVolume 20Number 6. Get permission to re-use this article. Sign up for new issue notifications. The advance publicity on the back of the dust jacket includes a commendation by Martin Gardner.
Gnomon: from pharaohs to fractals – PDF Free Download
In the s I used to await fraftals the arrival of Scientific Americanin which Gardner’s Mathematical Games column was an unfailing star. This book is of a similar quality and scope.
He discusses briefly the shape of the Great Pyramid. Its height was originally royal cubits, and its base royal cubits.
From this the slope can be found: 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. Iteration is a theme which runs through the book.
Gnomon: From Pharaohs to Fractals – Midhat J. Gazalé – Google Books
There is considerable discussion of continued fractions and of iterated roots e. 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 gnompn new to me.
Gnomon: from pharaohs to fractals
The discussion extends to mechanical ladder networks: There appear to be several silver numbers. Manfred Schroeder, in his entertaining book Fractals, Chaos and Power Laws Freeman, has a completely different definition of a silver number.
The level of this book is variable: In other places his pace is almost too slow; he devotes a full page to an explicit conversion of to a binary representation. 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 gnojon web site on which corrections to misprints can be shown: I have enjoyed reading and reviewing this book.
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