000 04468nam a22005535i 4500
001 978-0-387-29555-8
003 DE-He213
005 20161121231024.0
007 cr nn 008mamaa
008 100301s2006 xxu| s |||| 0|eng d
020 _a9780387295558
_9978-0-387-29555-8
024 7 _a10.1007/0-387-29555-0
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
245 1 0 _aNon-Euclidean Geometries
_h[electronic resource] :
_bJános Bolyai Memorial Volume /
_cedited by András Prékopa, Emil Molnár.
264 1 _aBoston, MA :
_bSpringer US,
_c2006.
300 _aXIII, 506 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematics and Its Applications ;
_v581
505 0 _aHistory -- 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.
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.
650 0 _aMathematics.
650 0 _aGeometry.
650 0 _aDifferential geometry.
650 0 _aHistory.
650 0 _aManifolds (Mathematics).
650 0 _aComplex manifolds.
650 0 _aGravitation.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
650 2 4 _aHistory of Mathematical Sciences.
650 2 4 _aDifferential Geometry.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
650 2 4 _aClassical and Quantum Gravitation, Relativity Theory.
700 1 _aPrékopa, András.
_eeditor.
700 1 _aMolnár, Emil.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387295541
830 0 _aMathematics and Its Applications ;
_v581
856 4 0 _uhttp://dx.doi.org/10.1007/0-387-29555-0
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c507420
_d507420