Non-Elucidean Geometrics : Janos Bolyai Memorial Volume

Janos Bolyai Memorial Volume

By: AndrÃ¡s PrÃ©kopa (Editor), Emil MolnÃ¡r (Editor)

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Hardcover | 1 November 2005

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524 Pages

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23.39 x 15.6 x 2.87

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"From nothing I have created a new different world," wrote J¡nos 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 J¡nos 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 J¡nos 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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Preface	p. xi
History
The Revolution of János Bolyai	p. 3
Gauss and non-Euclidean geometry	p. 61
János Bolyai's new face	p. 81
Axiomatical and Logical Aspects
Hyperbolic Geometry, Dimension-Free	p. 97
An Absolute Property of Four Mutually Tangent Circles	p. 109
Remembering Donald Coxeter	p. 115
Axiomatizations of hyperbolic and absolute geometries	p. 119
Logical axiomatizations of space-time. Samples from the literature	p. 155
Polyhedra, Volumes, Discrete Arrangements, Fractals
Structures in Hyperbolic Space	p. 189
The Symmetry of Optimally Dense Packings	p. 197
Flexible Octahedra in the Hyperbolic Space	p. 209
Fractal Geometry On Hyperbolic Manifolds	p. 227
A volume formula for generalised hyperbolic tetrahedra	p. 249
Tilings, Orbifolds and Manifolds, Visualization
The Geometry of Hyperbolic Manifolds of Dimension at least 4	p. 269
Real-Time Animation in Hyperbolic, Spherical, and Product Geometries	p. 287
On spontaneous surgery on knots and links	p. 307
Classification of tile-transitive 3-simplex tilings and their realizations	p. 321
Differential Geometry
Non-Euclidean Analysis	p. 367
Holonomy, geometry and topology of manifolds with Grassmann structure	p. 385
Hypersurfaces of type number 2 in the hyperbolic four-space	p. 407
How far does hyperbolic geometry generalize?	p. 427
Geometry of the point Finsler spaces	p. 445
Physics
Black hole perturbations	p. 465
An Idea Whose Time Has Returned	p. 487
Table of Contents provided by Publisher. All Rights Reserved.

Non-Elucidean Geometrics : Janos Bolyai Memorial Volume

Janos Bolyai Memorial Volume

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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