Non-Euclidean Geometries János Bolyai Memorial Volume /

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Prékopa, András (Επιμελητής έκδοσης), Molnár, Emil (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston, MA : Springer US, 2006.
• Σειρά: Mathematics and Its Applications ; 581
• Θέματα: Mathematics.; Geometry.; Differential geometry.; History.; Manifolds (Mathematics).; Complex manifolds.; Gravitation.; History of Mathematical Sciences.; Differential Geometry.; Manifolds and Cell Complexes (incl. Diff.Topology).; Classical and Quantum Gravitation, Relativity Theory.

"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...

Πίνακας περιεχομένων:

• 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.