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
Published: New York, NY Springer US 2006, 2006
Edition:1st ed. 2006
Series:Mathematics and Its Applications
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of 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 Homoge