Indra's Pearls
The Vision of Felix Klein
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Estimated delivery time: In stock at the publisher, but not at Prospero's office. Delivery time approx. 3-5 weeks.
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Product details:
- Publisher Cambridge University Press
- Date of Publication 25 April 2002
- ISBN 9780521352536
- Binding Hardback
- No. of pages418 pages
- Size 254x202x27 mm
- Weight 1197 g
- Language English
- Illustrations 55 b/w illus. 150 colour illus. 75 exercises 0
Categories
Short description:
This book tells the story of the first computer exploration of Klein's vision of infinitely repeated reflections, featuring extraordinary images.
MoreLong description:
Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.
'[This book is] richly illustrated with these wonderful and mysterious pictures and gives detailed instructions for recreating them, right down to the level of computer programs (written in pseudo-code, and easy to translate into any computer language) ... the reader who attempts any substantial subset of [the projects] will gain enormously ... Even those who are convinced they have no ability to visualize may change their minds ... It is almost required reading for the experts in the field ... I truly love this book.' John H. Hubbard, The American Mathematical Monthly
Table of Contents:
Preface; Introduction; 1. The language of symmetry; 2. A delightful fiction; 3. Double spirals and M&&&246;bius 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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