Non-Euclidean Geometries: János Bolyai Memorial Volume

Portada
András Prékopa, Emil Molnár
Springer Science & Business Media, 3 de juny 2006 - 506 pŕgines
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"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture.

The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

 

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Continguts

Physics
11
Gauss and nonEuclidean geometry
61
Janos Bolyais new face
81
Hyperbolic Geometry DimensionFree
97
Remembering Donald Coxeter
115
Logical axiomatizations of spacetime Samples from the literature
155
Structures in Hyperbolic Space
189
Flexible Octahedra in the Hyperbolic Space 209
208
RealTime Animation in Hyperbolic Spherical and Product Geometries
287
On spontaneous surgery on knots and links
307
Classification of tiletransitive 3simplex tilings and their realizations 321
325
NonEuclidean Analysis 367
365
Holonomy geometry and topology of manifolds with Grassmann structure
385
Hypersurfaces of type number 2 in the hyperbolic fourspace
407
How far does hyperbolic geometry generalize?
427
Geometry of the point Finsler spaces
445

Fractal Geometry On Hyperbolic Manifolds
227
A volume formula for generalised hyperbolic tetrahedra 249
248
The Geometry of Hyperbolic Manifolds of Dimension at least 4 269
267
Black hole perturbations
465
An Idea Whose Time Has Returned 487
486
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