Indra's pearls: the vision of Felix Klein
Publication details: Cambridge University Press, 2015. Cambridge;Description: xix, 395 p. : ill. ; pb, 26 cmISBN:- 9781107564749
- 514.742 MUM
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IIT Gandhinagar General Stacks | General | 514.742 MUM (Browse shelf(Opens below)) | 1 | Available | 030042 |
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514.74 PAT Geodesic flows | 514.742 BIS Fractals in probability and analysis | 514.742 FEL Chaos and dynamical systems: lessons for complex systems | 514.742 MUM Indra's pearls: the vision of Felix Klein | 515. 243 DAV Summation of series | 515 DAV Integral transforms and their applications | 515 DUD Real analysis and probability |
Includes bibliographical references and index.
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.
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