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Indra's Pearls : The Vision of Felix Klein

Indra's Pearls : The Vision of Felix Klein - 02 edition

Indra's Pearls : The Vision of Felix Klein - 02 edition

ISBN13: 9780521352536

ISBN10: 0521352533

Indra
Edition: 02
Copyright: 2002
Publisher: Cambridge University Press
Published: 2002
International: No
Indra

ISBN13: 9780521352536

ISBN10: 0521352533

Summary

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.

Table of Contents

Table of Contents

1. The language of symmetry
2. A delightful fiction
3. Double spirals and Möbius maps
4. The Schottky dance
5. Fractal dust and infinite words
6. Indra's necklace
7. The glowing gasket
8. Playing with parameters
9. Accidents will happen
10. Between the cracks
11. Crossing boundaries
12. Epilogue
Index
Road map.

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