The beaver's tooth and the tiger's claw. Sunflowers and seashells. Fractals, Fibonacci sequences, and logarithmic spirals. These diverse forms of nature and mathematics are united by a common factor: all involve self-repeating shapes, or gnomons.
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View Larger Image. Ask Seller a Question. Title: Gnomon From Pharaohs to Fractals. Publisher: Princeton U. The beaver's tooth and the tiger's claw.
Sunflowers and seashells. Fractals, Fibonacci sequences, and logarithmic spirals. These diverse forms of nature and mathematics are united by a common factor: all involve self-repeating shapes, or gnomons.
Almost two thousand years ago, Hero of Alexandria defined the gnomon as that form which, when added to some form, results in a new form, similar to the original. In a spiral seashell, for example, we see that each new section of growth the gnomon resembles its predecessor and maintains the shell's overall shape. He has a passion for numbers that is clear on every page, as he combines elegant mathematical explanations with compelling anecdotes and a rich variety of illustrations.
He begins by explaining the basic properties of gnomons and tracing the term--which originally meant "that which allows one to know"--to ancient Egyptian and Greek timekeeping.
He introduces us to continued fractions and guides us through the intricacies of Fibonacci sequences, ladder networks, whorled figures, the famous "golden number," logarithmic spirals, and fractals. This is an erudite, engaging, and beautifully produced work that will appeal to anyone interested in the wonders of geometry and mathematics, as well as to enthusiasts of mathematical puzzles and recreations.
How are the great pyramids like seashells? 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 paean to the roiling mysteries that lie beneath the tranquil surfaces of such objects.
The great mathematician Hero of Alexandria defined a gnomon as an object that, when added to another, creates a new object similar in form to the original. Gazale, also of Alexandria, goes much further and uses 20th-century concepts to fully explore "gnomonicity"--the property of self-similarity. Be prepared for slow going: Gnomon is densely packed with information and concepts foreign to all but the professional mathematician, but Gazale's enthusiasm and brilliant illustrations win the day.
Whether he's moving on from the familiar golden rectangle to his own "silver pentagon" or rooting around in the numbers underlying the groovy fractal images popping up on T-shirts worldwide, he takes care to explain to the reader not just what's going on mathematically but what all this abstraction really means to us. Few science books, and even fewer mathematics books, achieve that kind of depth.
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Midhat J. Gazalé
In the words of the author "The theme of this book is self-similarity, which I call gnomonicity. The connotation of the term gnomon is that originally given by Hero of Alexandria, namely, 'A Gnomon is that form that, when added to some form, results in a new form similar to the original. The most familiar form of a gnomon is the L-shaped object of that name the gnomon of a square that serves as the pointer on most sundials. This observation virtually completes the "Pharaohs" end of the story mentioned in the title.
Gnomon: From Pharaohs to Fractals
Published by Princeton U. Press, rinceton, NJ Seller Rating:. About this Item: Princeton U. Press, rinceton, NJ,