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Book Cover
E-book
Author Mumford, David, 1937-

Title Indra's pearls : the vision of Felix Klein / David Mumford, Caroline Series and David Wright ; with cartoons by Larry Gonick
Published Cambridge : Cambridge University Press, 2002

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Description 1 online resource (xix, 395 pages) : illustrations (some color)
Contents The language of symmetry -- A delightful fiction -- Double spirals and Möbius maps -- The Schottky dance -- Fractal dust and infinite words -- Indra's necklace -- The glowing gasket -- Playing with parameters -- Accidents will happen -- Between the cracks -- Crossing boundaries -- Epilogue -- Index -- Road map
Summary "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 co-existing symmetries, each simple in itself, but whose interactions produce fractals on the edge of chaos. For a century these images, which were practically impossible to draw by hand, 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 so doing found further extraordinary images of their own. Join the authors on the path from some basic mathemathical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can learn to understand what the images mean and follow the step-by-step instructions for writing computer programs that generate them. More advanced readers can see how the images relate to ideas that take them to the forefront of research."--Jacket
Notes Includes index
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Klein, Felix, 1849-1925.
SUBJECT Klein, Felix, 1849-1925 fast
Subject Geometry.
Symmetry.
Indra (Hindu deity)
Fractals.
geometry.
fractals.
MATHEMATICS -- Topology.
Fractals
Geometry
Indra (Hindu deity)
Symmetry
Fraktalgeometrie
Parels.
Geometria.
Grupos de klein.
Form Electronic book
Author Series, Caroline
Wright, David James.
Gonick, Larry
LC no. 2002510876
ISBN 9780511065309
0511065302
9781107050051
1107050057
9780511067433
0511067437
9781107712683
1107712688
9781107564749
1107564743