## Indra's Pearls: The Vision of Felix KleinFelix 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. |

### Contents

The language of symmetry | 1 |

A delightful fiction | 36 |

Double spirals and Möbius maps | 62 |

The Schottky dance | 96 |

Fractal dust and infinite words | 121 |

Indras necklace | 157 |

The glowing gasket 196 | 196 |

Playing with parameters | 224 |

### Other editions - View all

Indra's Pearls: The Vision of Felix Klein David Mumford,Caroline Series,David Wright Limited preview - 2002 |

Indra's Pearls: The Vision of Felix Klein David Mumford,Caroline Series,David Wright No preview available - 2015 |

Indra's Pearls: The Vision of Felix Klein David Mumford,Caroline Series,David James Wright,David Wright No preview available - 2002 |

### Common terms and phrases

abAB actually algorithm angle applying basic beginning blue boundary calculate called carries centre Chapter circles close coloured complex numbers conjugate contains corresponding curve cusp described disks draw equation exactly example explained fact Figure fixed point formula four fractal fractions frame gasket geometry gives idea infinite infinite words initial inside interesting inverse labelled limit points limit set look mathematical matrix means method Möbius maps move multiply nesting Note original pair parabolic path pattern picture plane plot positive possible Project recipe region represent result rotation rule Schottky Schottky circles sequence shown shows side solution sphere spiral square starting step Suppose surface symmetry tangent thing tile trace transformation translation tree turns unit whole write

### References to this book

Non-Euclidean Geometries: János Bolyai Memorial Volume András Prékopa,Emil Molnár No preview available - 2006 |