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Indra's Pearls: The Vision of Felix Kleinby David Mumford and Caroline Series and Davis Wright
Synopses & Reviews
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.
Highly illustrated realization of infinitely reflected images related to fractals, chaos and symmetry.
Felix Klein 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. The whole Universe was mirrored in each pearl. For a century this idea, practically impossible to represent by hand, barely existed outside the imagination of mathematicians. In the 1980s the authors embarked on the first computer exploration of Kleinâ€™s vision. Join them on the path from simple mathematics to computer programs that generate these images related to ideas at the forefront of knowledge.
For a century Klein's vision of infinately repeated reflections, practically impossible to represent by had, barely existed outside the imagination of mathematicians, In the 1980's the authors embarked on the first computer exploration of Klein's vision, here available for the first time in print, with the programs that generate them.
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.
About the Author
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 35 years. He has received many honours for his mathematical work, including a Fields medal in 1974. He has been a contributor to the Calculus Textbook Project, led by Hughes-Hallet and Gleason.
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.
David Wright is Associate Professior at Oklahoma State University. He has a guest professorship at the University of Göttingen, and was Sloan Fellow at the Institute for Advanced study in Princeton from 1988 to 1990. From 1997 to 1999 he helped compose the famous William Lowell Putnam Mathematical Competition.
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
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