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David Mumford, Caroline Series, David Wright, "Indra's Pearls: The Vision of Felix Klein"

Description

Felix Klein, a great geometer of the nineteenth century, rediscovered an idea from Hindu mythology in mathematics: the heaven of Indra in which the whole Universe was mirrored in each pearl in a net of pearls. Practically impossible to represent by hand, this idea barely existed outside the imagination, until the 1980s when the authors embarked on the first computer investigation of Klein's vision. In this extraordinary book they explore the path from some basic mathematical ideas to the simple algorithms that create delicate fractal filigrees, most appearing in print for the first time. Step-by-step instructions for writing computer programs allow beginners to generate the images.

Reviews

"I truly love this book...a magnificent text." American Mathematical Monthly

"It has been a great pleasure to read such a gracefully written, original book of mathematics. The three authors, with the support of Cambridge University Press, have produced a book that is as handsome in physical appearance as its content is stimulating and accessible. The book is an exemplar of its genre and a singular contribution to the contemporary mathematics literature." Notices of the AMS

"The production of the book leaves nothing to be desired. It is spendid. Printed entirely on glossy paper, with practically all of the many figures in glorious color, the book has a number of admirable design features: large type and wide margins wherein references are given and occasional comments (often quite talky) are made. CU Press has done a beautiful job, and David Tranah of the CU Press deserves special commendation for his role in pulling out all the stops." SIAM News

"All of it is patiently explained...By the time you finish, you'll know your way around this complex plane." American Scientist

"...raises a number of interesting issues... The book itself is a work of art... I truly enjoyed reading Indra's Pearls. I am sure that the book will have a major impact on the way we teach geometry and dynamics...a jewel that will more than repay the persistent reader's efforts." Science

"This book is written as a guide to actually coding the algorithms which are used to generate the delicate fractal filigrees, most of which have never appeared in print before....Beginners can learn to understand what the images mean and follow the step-by-step instructions for writing computer programs that generate them. Experts in the geometry of discrete groups can see how the images relate to ideas that take them to the forefront of research." Mathematical Reviews

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