Noneuclidean Tesselations and Their Groups
Academic Press
Published on 18. October 1974
206 pages
978-0-08-087377-0 (ISBN)
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Noneuclidean Tesselations and Their Groups
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Wilhelm Magnus
Non-Euclidean Tesselations and Their Groups
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01/1974
Academic Press
€55.71
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Content
- Front Cover
- Noneuclidean Tesselations and Their Groups
- Copyright Page
- Contents
- Preface
- Abbreviations and Symbols
- CHAPTER I. ELEMENTARY CONCEPTS AND FORMULAS
- I.1 The Group G* of Homographic Substitutions
- I.2 Action of G* on the Closed Complex Plane C
- I.3 Action of G* on Hyperbolic Three-Space
- I.4 Circle Groups as Groups of Motions of Hyperbolic Two-Space
- I.5 Notes on Elliptic and Spherical Geometry
- I.6 Illustrations. References and Historical Remarks
- I.7 Appendix: Hilbert's Axioms of Geometry
- CHAPTER II. DISCONTINUOUS GROUPS AND TRIANGLE TESSELATIONS
- II.1 Introductory Remarks
- II.2 Discontinuous Groups and Fundamental Regions
- II.3 Triangle Groups, Local and Global Relations
- II.4 Euclidean, Spherical, and Elliptic Triangle Groups
- II.5 Hyperbolic Triangle Groups
- II.6 Some Subgroups of Hyperbolic Triangle Groups
- II.7 General Theorems. A Survey and References
- CHAPTER III. NUMBER THEORETICAL METHODS
- III.1 The Modular Group
- III.2 Subgroups and Quotient Groups of the Modular Group
- III.3 Groups of Units of Ternary Quadratic and Binary Hermitian Forms
- CHAPTER IV. MISCELLANY
- IV.1 Examples of Discontinuous Nonfuchsian Groups
- IV.2 Fricke Characters
- CHAPTER V. GROUPS THAT ARE DISCONTINUOUS IN HYPERBOLIC THREE-SPACE
- V.l Linear Groups over Imaginary Quadratic Number Fields
- V.2 Some Geometric Contructions
- Figures
- References
- Index
