Title Non-Euclidean geometries : János Bolyai memorial volume / edited by András Prékopa, Emil Molnár

Published New York : Springer, ©2006

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Description 1 online resource (xiii, 506 pages) : illustrations, facsimiles Series Mathematics and its applications ; v. 581 Mathematics and its applications (Springer Science+Business Media) ; 581. Contents History -- The Revolution of János Bolyai -- Gauss and Non-Euclidean Geometry -- János Bolyai's New Face -- Axiomatical and Logical Aspects -- Hyperbolic Geometry, Dimension-Free -- An Absolute Property of Four Mutually Tangent Circles -- Remembering Donald Coxeter -- Axiomatizations of Hyperbolic and Absolute Geometries -- Logical Axiomatizations of Space-Time. Samples from the Literature -- Polyhedra, Volumes, Discrete Arrangements, Fractals -- Structures in Hyperbolic Space -- The Symmetry of Optimally Dense Packings -- Flexible Octahedra in the Hyperbolic Space -- Fractal Geometry on Hyperbolic Manifolds -- A Volume Formula for Generalised Hyperbolic Tetrahedra -- Tilings, Orbifolds and Manifolds, Visualization -- The Geometry of Hyperbolic Manifolds of Dimension at Least 4 -- Real-Time Animation in Hyperbolic, Spherical, and Product Geometries -- On Spontaneous Surgery on Knots and Links -- Classification of Tile-Transitive 3-Simplex Tilings and Their Realizations in Homogeneous Spaces -- Differential Geometry -- Non-Euclidean Analysis -- Holonomy, Geometry and Topology of Manifolds with Grassmann Structure -- Hypersurfaces of Type Number 2 in the Hyperbolic Four-Space and Their Extensions To Riemannian Geometry -- How Far Does Hyperbolic Geometry Generalize? -- Geometry of the Point Finsler Spaces -- Physics -- Black Hole Perturbations -- Placing the Hyperbolic Geometry of Bolyai and Lobachevsky Centrally in Special Relativity Theory: An Idea Whose Time has Returned Summary "The papers in this volume, which commemorates the 200th anniversary of the birth of Janos 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 Janos 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. Audience This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information."--Publisher's website Notes Published in conjunction with an international conference on hyperbolic geometry, held July 6-12, 2002 in Budapest and organized by the Hungarian Academy of Sciences and other institutions Bibliography Includes bibliographical references Notes Print version record In Springer e-books Subject Bolyai, János, 1802-1860 -- Congresses SUBJECT Bolyai, János, 1802-1860. cct Bolyai, János, 1802-1860 fast Subject Geometry, Non-Euclidean -- Congresses Geometry, Hyperbolic -- Congresses MATHEMATICS -- Geometry -- Non-Euclidean. Geometry, Hyperbolic. Geometry, Non-Euclidean. Geometría no euclidiana -- Congresos Geometría hiperbólica -- Congresos Geometry, Hyperbolic Geometry, Non-Euclidean Genre/Form proceedings (reports) Festschriften Conference papers and proceedings Conference papers and proceedings. Festschriften. Actes de congrès. Form Electronic book Author Bolyai, János, 1802-1860. Prékopa, A. (András), 1929- Molnár, Emil Magyar Tudományos Akadémia. LC no. 2005933885 ISBN 9780387295558 0387295550 9780387295541 0387295542 661060939X 9786610609390

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