The Vision of Felix Klein
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Indra's Pearls by David Mumford
Book DescriptionFelix 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.
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Book DetailsISBN: 9780521352536
(246mm x 189mm x 32mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 25-Apr-2002
Country of Publication: United Kingdom
Books By Author David Mumford
Indra's Pearls, Paperback (November 2015)
This book tells the story of the first computer exploration of Klein's vision of infinitely repeated reflections, featuring extraordinary images.
Best Writing on Mathematics, Paperback (November 2012)
Offers surprising insights into the nature, meaning, and practice of mathematics. This book explains mathematical aspects of origami foldings; discusses the frequency and distribution of the prime numbers; ponders whether mathematics is invented or discovered; and describes what is special about a ball in five dimensions.
Smooth Compactifications of Locally Symmetric Varieties, Paperback (January 2010)» View all books by David Mumford
The classic presentation of a universal method for the resolution of a class of singularities in algebraic geometry.
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Author Biography - David Mumford
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 Gottingen, 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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