Indra's pearls : the vision of Felix Klein

David Mumford, Caroline Series and David Wright ; with cartoons by Larry Gonick

Felix Klein, one of the great nineteenth-century geometers, rediscovered in mathematics an idea from Eastern philosophy: 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 co-existing symmetries. For a century these ideas 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.

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  • 1. The language of symmetry
  • 2. A delightful fiction
  • 3. Double spirals and Mobius 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.

「Nielsen BookData」より


書名 Indra's pearls : the vision of Felix Klein
著作者等 Gonick, Larry
Mumford, David
Series, Caroline
Wright, David
出版元 Cambridge University Press
刊行年月 2002
ページ数 xix, 395 p.
大きさ 26 cm
ISBN 9780521352536
NCID BA56484936
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言語 英語
出版国 イギリス