Non-Euclidean Geometries : János Bolyai Memorial Volume

"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...

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Corporate Author: SpringerLink (Online service)
Other Authors: Prékopa, András (Editor), Molnár, Emil (Editor)
Format: eBook
Language:English
Published: New York, NY Springer US 2006, 2006
Edition:1st ed. 2006
Series:Mathematics and Its Applications
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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505 0 |a 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 Homoge 
653 |a Differential Geometry 
653 |a Global differential geometry 
653 |a History of Mathematical Sciences 
653 |a Cell aggregation / Mathematics 
653 |a Geometry 
653 |a Classical and Quantum Gravitation, Relativity Theory 
653 |a Geometry 
653 |a Manifolds and Cell Complexes (incl. Diff.Topology) 
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520 |a "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. 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