03127nam 2200601Ia 450 991078233570332120230120005813.01-281-76658-597866117665800-08-087377-4(CKB)1000000000551621(EBL)404864(OCoLC)476220393(SSID)ssj0000389759(PQKBManifestationID)12120569(PQKBTitleCode)TC0000389759(PQKBWorkID)10463829(PQKB)10745928(MiAaPQ)EBC404864(EXLCZ)99100000000055162119941123d1974 uy 0engur|n|---|||||txtccrNoneuclidean tesselations and their groups[electronic resource] /Wilhelm MagnusNew York ;London Academic Press19741 online resource (225 p.)Pure and applied mathematics ;61Description based upon print version of record.0-12-465450-9 Includes bibliography and index.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 RemarksII.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 CharactersCHAPTER V. GROUPS THAT ARE DISCONTINUOUS IN HYPERBOLIC THREE-SPACEV.l Linear Groups over Imaginary Quadratic Number Fields; V.2 Some Geometric Contructions; Figures; References; IndexNoneuclidean tesselations and their groupsPure and Applied MathematicsTessellations (Mathematics)Geometry, Non-EuclideanTessellations (Mathematics)Geometry, Non-Euclidean.510.8 s511.6510/.8 s 511/.6516.9Magnus Wilhelm1907-1990.6717MiAaPQMiAaPQMiAaPQBOOK9910782335703321Noneuclidean Tesselations and Their Groups979052UNINA