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Non-Euclidean Geometries

János Bolyai Memorial Volume

  • Book
  • © 2006

Overview

Editors:
  1. András Prékopa

    1. Rutgers Center for Operations Research, Piscataway, USA

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  2. Emil Molnár

    1. Budapest University of Technology and Economics, Hungary

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  • Focuses specifically on the contributions of János Bolyai to non-Euclidean geometry
  • Includes supplementary material: sn.pub/extras

Part of the book series: Mathematics and Its Applications (MAIA, volume 581)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xiii
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  2. History

    1. Front Matter

      Pages 1-1
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    2. The Revolution of János Bolyai

      • András Prékopa
      Pages 3-59

    3. Gauss and Non-Euclidean Geometry

      • Jeremy Gray
      Pages 61-80

    4. János Bolyai’s New Face

      • Elemér Kiss
      Pages 81-93

  3. Axiomatical and Logical Aspects

    1. Front Matter

      Pages 95-95
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    2. Hyperbolic Geometry, Dimension-Free

      • Walter Benz
      Pages 97-107

    3. An Absolute Property of Four Mutually Tangent Circles

      • H.S.M. Coxeter
      Pages 109-114

    4. Remembering Donald Coxeter

      • Asia Ivic Weiss, William Weiss
      Pages 115-118

    5. Axiomatizations of Hyperbolic and Absolute Geometries

      • Victor Pambuccian
      Pages 119-153

    6. Logical Axiomatizations of Space-Time. Samples from the Literature

      • Hajnal Andréka, Judit X. Madarász, István Németi
      Pages 155-185

  4. Polyhedra, Volumes, Discrete Arrangements, Fractals

    1. Front Matter

      Pages 187-187
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    2. Structures in Hyperbolic Space

      • Robert Connelly
      Pages 189-196

    3. The Symmetry of Optimally Dense Packings

      • Charles Radin
      Pages 197-207

    4. Flexible Octahedra in the Hyperbolic Space

      • Hellmuth Stachel
      Pages 209-225

    5. Fractal Geometry on Hyperbolic Manifolds

      • Bernd O. Stratmann
      Pages 227-247

    6. A Volume Formula for Generalised Hyperbolic Tetrahedra

      • Akira Ushijima
      Pages 249-265

  5. Tilings, Orbifolds and Manifolds, Visualization

    1. Front Matter

      Pages 267-267
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    2. The Geometry of Hyperbolic Manifolds of Dimension at Least 4

      • John G. Ratcliffe
      Pages 269-286

    3. Real-Time Animation in Hyperbolic, Spherical, and Product Geometries

      • Jeffrey R. Weeks
      Pages 287-305
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Keywords

About this book

"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.

Editors and Affiliations

  • Rutgers Center for Operations Research, Piscataway, USA

    András Prékopa

  • Budapest University of Technology and Economics, Hungary

    Emil Molnár

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