Indra's Pearls: The Vision of Felix Klein

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Cambridge University Press, Apr 25, 2002 - Mathematics - 395 pages
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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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User Review  - fpagan - LibraryThing

Mathematical and algorithmic details of a lesser-known class of fractals. Quite lavishly produced. Read full review

Contents

The language of symmetry
1
A delightful fiction
36
Double spirals and Möbius maps
62
The Schottky dance
96
Fractal dust and infinite words
121
Indras necklace
157
The glowing gasket 196
196
Playing with parameters
224
Accidents will happen
268
Between the cracks
310
Crossing boundaries
353
Epilogue
373
Index
394
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About the author (2002)

David Mumford has been University Professor in the Division of Applied Mathematics at Brown University since 1996. Before that he was at Harvard University for thirty-five years. He has been a contributor to the Calculus Textbook Project, led by Hughes-Hallett and Gleason. Over his long and distinguished career, Professor Mumford has received many awards and honours, including the Fields Medal in 1974, the Wolf Prize in 1998 and the National Medal of Science in 2010.

Caroline Series is Professor of Mathematics at Warwick University where she currently holds an EPSRC Senior Research Fellowship. She was Kennedy Scholar at Harvard University from 1972 to 1974. In addition to technical publications, she has contributed widely to the popularization of mathematics. In 2014, she won the first Senior Anne Bennett Prize of the London Mathematical Society for contributions to mathematics and to the advancement of female mathematicians. She edits the new International Women in Maths website http://www.mathunion.org/wim/.

David Wright is Professor at Oklahoma State University. He has held a guest professorship at the University of G ttingen, and was Sloan Fellow at the Institute for Advanced Study in Princeton from 1988 to 1990. From 1997 to 1999 he helped establish the famous William Lowell Putnam Mathematical Competition. In 2009 he received a Distinguished Teaching Award from the Mathematical Association of America.

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