Non-Euclidean Geometries

János Bolyai Memorial Volume

Editors:

ISBN: 978-0-387-29554-1 (Print) 978-0-387-29555-8 (Online)

Table of contents (24 chapters)

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  1. History

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-59

      The Revolution of János Bolyai

    3. No Access

      Book Chapter

      Pages 61-80

      Gauss and Non-Euclidean Geometry

    4. No Access

      Book Chapter

      Pages 81-93

      János Bolyai’s New Face

  2. Axiomatical and Logical Aspects

    1. Front Matter

      Pages 95-95

    2. No Access

      Book Chapter

      Pages 97-107

      Hyperbolic Geometry, Dimension-Free

    3. No Access

      Book Chapter

      Pages 109-114

      An Absolute Property of Four Mutually Tangent Circles

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      Book Chapter

      Pages 115-118

      Remembering Donald Coxeter

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      Book Chapter

      Pages 119-153

      Axiomatizations of Hyperbolic and Absolute Geometries

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      Book Chapter

      Pages 155-185

      Logical Axiomatizations of Space-Time. Samples from the Literature

  3. Polyhedra, Volumes, Discrete Arrangements, Fractals

    1. Front Matter

      Pages 187-187

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      Book Chapter

      Pages 189-196

      Structures in Hyperbolic Space

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      Book Chapter

      Pages 197-207

      The Symmetry of Optimally Dense Packings

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      Book Chapter

      Pages 209-225

      Flexible Octahedra in the Hyperbolic Space

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      Book Chapter

      Pages 227-247

      Fractal Geometry on Hyperbolic Manifolds

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      Book Chapter

      Pages 249-265

      A Volume Formula for Generalised Hyperbolic Tetrahedra

  4. Tilings, Orbifolds and Manifolds, Visualization

    1. Front Matter

      Pages 267-267

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      Book Chapter

      Pages 269-286

      The Geometry of Hyperbolic Manifolds of Dimension at Least 4

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      Book Chapter

      Pages 287-305

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

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      Book Chapter

      Pages 307-319

      On Spontaneous Surgery on Knots and Links

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      Book Chapter

      Pages 321-363

      Classification of Tile-Transitive 3-Simplex Tilings and Their Realizations in Homogeneous Spaces

  5. Differential Geometry

    1. Front Matter

      Pages 365-365

    2. No Access

      Book Chapter

      Pages 367-384

      Non-Euclidean Analysis

    3. No Access

      Book Chapter

      Pages 385-405

      Holonomy, Geometry and Topology of Manifolds with Grassmann Structure

    4. No Access

      Book Chapter

      Pages 407-426

      Hypersurfaces of Type Number 2 in the Hyperbolic Four-Space and Their Extensions To Riemannian Geometry

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