03285nam 2200709Ia 450 991082277430332120200520144314.01-107-71306-40-511-05897-71-107-71268-80-511-06743-71-107-71814-70-511-06530-21-107-05005-70-511-15720-7(CKB)1000000000003980(EBL)217854(SSID)ssj0000280750(PQKBManifestationID)11912436(PQKBTitleCode)TC0000280750(PQKBWorkID)10299912(PQKB)11024140(UkCbUP)CR9781107050051(Au-PeEL)EBL217854(CaPaEBR)ebr10014603(CaONFJC)MIL589058(OCoLC)70763570(MiAaPQ)EBC217854(PPN)261340832(EXLCZ)99100000000000398020020524d2002 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierIndra's pearls the vision of Felix Klein /David Mumford, Caroline Series and David Wright ; with cartoons by Larry Gonick1st ed.Cambridge Cambridge University Press20021 online resource (xix, 395 pages) digital, PDF file(s)Includes index.1-107-56474-3 0-521-35253-3 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.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 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.GeometrySymmetryIndra (Hindu deity)Geometry.Symmetry.Indra (Hindu deity)514/.742Mumford David1937-42095Series Caroline283926Wright David354509MiAaPQMiAaPQMiAaPQBOOK9910822774303321Indra's pearls4191244UNINA