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100   $a20020524d2002      uy         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aIndra's pearls $ethe vision of Felix Klein /$fDavid Mumford, Caroline Series and David Wright ; with cartoons by Larry Gonick
205   $a1st ed.
210   $aCambridge $cCambridge University Press$d2002
215   $a1 online resource (xix, 395 pages) $cdigital, PDF file(s)
300   $aIncludes index.
311   $a1-107-56474-3 
311   $a0-521-35253-3 
327   $aThe language of symmetry -- A delightful fiction -- Double spirals and Mo?bius 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.
330   $aFelix 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.
606   $aGeometry
606   $aSymmetry
606   $aIndra (Hindu deity)
615  0$aGeometry.
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615  0$aIndra (Hindu deity)
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700   $aMumford$b David$f1937-$042095
701   $aSeries$b Caroline$0283926
701   $aWright$b David$0354509
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996   $aIndra's pearls$94191244
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