Indra's Pearls: The Vision of Felix KleinFelix 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. |
Other editions - View all
Indra's Pearls: The Vision of Felix Klein David Mumford,Caroline Series,David James Wright,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 algebra algorithm angle Apollonian gasket baBA blue boundary calculate called centre chain Chapter coloured complex numbers conjugate corresponding curve cusp groups cyclic permutations depth-first search equation exactly example Farey Farey sequence fixed point formula fractal fractions frame of Figure Fuchsian geometry glue gluing Grandma's half plane Hausdorff dimension hyperbolic ideal triangle infinite words inside integer inverse Klein Kleinian groups labelled limit points limit set look loop loxodromic Maskit mathematical mathematician matrix Möbius maps Möbius transformation modular group move multiply nesting non-Euclidean ordinary set p/q word pair parabolic parameters pattern picture plot quasicircle radius real numbers recipe region repetends Riemann sphere rotation Schottky circles Schottky disks Schottky group segment sequence shows slice spiral stereographic projection Stickler symmetry t₁ tangency points tangent tangent circles tile torus trace translation unit circle vertical word tree