Indra's Pearls

The Vision of Felix Klein

AvDavid Mumford,Caroline Series

Häftad, Engelska, 2015

528 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Inbunden

1 169 kr

Beskrivning

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.

Produktinformation

Utgivningsdatum:2015-11-05
Mått:190 x 248 x 21 mm
Vikt:1 162 g
Format:Häftad
Språk:Engelska
Antal sidor:414
Förlag:Cambridge University Press
ISBN:9781107564749

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

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 Göttingen, 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.

Recensioner i media

'[This book is] richly illustrated with these wonderful and mysterious pictures and gives detailed instructions for recreating them, right down to the level of computer programs (written in pseudo-code, and easy to translate into any computer language) … the reader who attempts any substantial subset of [the projects] will gain enormously … Even those who are convinced they have no ability to visualize may change their minds … It is almost required reading for the experts in the field … I truly love this book.' John H. Hubbard, The American Mathematical Monthly

Innehållsförteckning

Preface; Introduction; 1. The language of symmetry; 2. A delightful fiction; 3. Double spirals and Möbius maps; 4. The Schottky dance; 5. Fractal dust and infinite words; 6. Indra's necklace; 7. The glowing gasket; 8. Playing with parameters; 9. Accidents will happen; 10. Between the cracks; 11. Crossing boundaries; 12. Epilogue; Index; Road map.