Noneuclidean tesselations and their groups / Wilhelm Magnus.

Format:

Book

Author/Creator:

Magnus, Wilhelm, 1907-1990.

Series:

Pure and Applied Mathematics

Pure and applied mathematics ; 61

Language:

English

Subjects (All):

Tessellations (Mathematics).

Geometry, Non-Euclidean.

Physical Description:

1 online resource (225 p.)

Place of Publication:

New York ; London : Academic Press, 1974.

Language Note:

English

Summary:

Noneuclidean tesselations and their groups

Contents:

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 RegionsII.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-SPACEV.l Linear Groups over Imaginary Quadratic Number Fields; V.2 Some Geometric Contructions; Figures; References; Index

Notes:

Description based upon print version of record.

Includes bibliography and index.

ISBN:

1-281-76658-5

9786611766580

0-08-087377-4

OCLC:

476220393