Indra's pearls : the vision of Felix Klein
著者
書誌事項
Indra's pearls : the vision of Felix Klein
Cambridge University Press, 2015, c2006
- : pbk
大学図書館所蔵 全1件
注記
Includes index
内容説明・目次
内容説明
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.
目次
- Preface
- Introduction
- 1. The language of symmetry
- 2. A delightful fiction
- 3. Double spirals and Moebius 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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