Indra's Pearls: The Vision of Felix Klein

Seitenzahl:

396

Gewicht:

1184 g

Erschienen bei:

Cambridge University Press

Inhaltsverzeichnis

From the contents:

1. 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

Kurzbeschreibung

Felix Klein, one of the great nineteenth-century geometers, rediscovered in mathematics an idea from Eastern philosophy: 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. For a century these ideas 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.

Portrait

David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics.§Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.

Mehr über...

Mehr über:  Mathematics, Klein, Felix, Mathematics / Algebra / General, Mathematics / Discrete Mathematics, Mathematics / Group Theory

Mehr von: 

Mehr von:  David Mumford, David Wright, Caroline Series, Cambridge University Press