Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Classical tessellations and three-manifolds / José María Montesinos
| Classical tessellations and three-manifolds / José María Montesinos |
| Autore | Montesinos, José María |
| Pubbl/distr/stampa | Berlin : Springer-Verlag, c1987 |
| Descrizione fisica | xvii, 230 p. : ill. ; 25 cm. |
| Disciplina | 514.223 |
| Collana | Universitext |
| Soggetto topico |
Tessellations (Mathematics)
Three-manifolds |
| ISBN | 3540152911 |
| Classificazione |
AMS 05B45
AMS 20F38 AMS 51F15 AMS 51M05 AMS 51M10 AMS 51M20 AMS 57M05 AMS 57M12 AMS 57M25 AMS 57N10 QA166.8.M66 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000744999707536 |
Montesinos, José María
|
||
| Berlin : Springer-Verlag, c1987 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Noneuclidean tesselations and their groups [[electronic resource] /] / Wilhelm Magnus
| Noneuclidean tesselations and their groups [[electronic resource] /] / Wilhelm Magnus |
| Autore | Magnus Wilhelm <1907-1990.> |
| Pubbl/distr/stampa | New York ; ; London, : Academic Press, 1974 |
| Descrizione fisica | 1 online resource (225 p.) |
| Disciplina |
510.8 s511.6
510/.8 s 511/.6 516.9 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Tessellations (Mathematics)
Geometry, Non-Euclidean |
| ISBN |
1-281-76658-5
9786611766580 0-08-087377-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910782335703321 |
|
Magnus Wilhelm <1907-1990.>
|
||
| New York ; ; London, : Academic Press, 1974 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Noneuclidean tesselations and their groups / / Wilhelm Magnus
| Noneuclidean tesselations and their groups / / Wilhelm Magnus |
| Autore | Magnus Wilhelm <1907-1990.> |
| Pubbl/distr/stampa | New York ; ; London, : Academic Press, 1974 |
| Descrizione fisica | 1 online resource (225 p.) |
| Disciplina |
510.8 s511.6
510/.8 s 511/.6 516.9 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Tessellations (Mathematics)
Geometry, Non-Euclidean |
| ISBN |
1-281-76658-5
9786611766580 0-08-087377-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910812387203321 |
|
Magnus Wilhelm <1907-1990.>
|
||
| New York ; ; London, : Academic Press, 1974 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Tilings of the plane : from Escher via Möbius to Penrose / / Ehrhard Behrends
| Tilings of the plane : from Escher via Möbius to Penrose / / Ehrhard Behrends |
| Autore | Behrends Ehrhard <1946-> |
| Pubbl/distr/stampa | Wiesbaden, Germany : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (284 pages) |
| Disciplina | 516.132 |
| Collana | Mathematics study resources |
| Soggetto topico |
Tessellations (Mathematics)
Mosaics (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783658388102
9783658388096 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- Part I Looking over Escher's Shoulder -- 2 Symmetries and Fundamental Domains -- 2.1 What is Symmetry? -- 2.2 What Movements are There? -- 2.3 Groups of Movements -- 2.4 Discontinuous Groups and Fundamental Domains -- 3 The Discontinuous Symmetry Groups of the Plane -- 3.1 How Many Different Groups of Movements are There? -- 3.2 Finite Groups of Movements -- 3.3 The Subgroup of Translations -- 3.4 The 7 Frieze Groups -- 3.4.1 : Only Translations -- 3.4.2 : Only Reflections of Type 1 () -- 3.4.3 : Only Reflections of Type 2 () -- 3.4.4 : Proper Glide Reflections () -- 3.4.5 : Only Rotations () -- 3.4.6 : Rotations, Type-1 and Type-2 Reflections () -- 3.4.7 : Proper Glide Reflections, Type-2 Reflections, and Rotations () -- 3.4.8 Summary -- 3.4.9 Classification: A Test -- 3.4.10 Hints for Artists -- 3.5 The 17 Plane Crystal Groups -- 3.5.1 The Crystallographic Restriction -- 3.5.2 Translations, Reflections: 4 Groups -- 3.5.3 Translations, 2-Rotations, Reflections: 5 Groups -- 3.5.4 Translations, 3-Rotations, (Glide) Reflections: 3 Groups -- 3.5.5 Translations, 4-Rotations, Reflections: 3 Groups -- 3.5.6 Translations, 6-Rotations, Reflections: 2 Groups -- 3.5.7 Classification: A Test -- 4 The Heesch Constructions -- 4.1 Lattices and Nets -- 4.2 The Heesch Construction: Motivation -- 4.3 The Heesch Constructions: 28 Methods -- References for Part I -- Part II Möbius Transformations -- 5 Möbius Transformations -- 5.1 Complex Numbers: Some Reminders -- 5.2 Möbius Transformations: Definitions and First Results -- 5.3 Möbius Transformations and Circles -- 5.4 Fixed Points of Möbius Transformations -- 5.5 Conjugate Möbius Transformations -- 5.6 Characterization: Fixed Points in {0,∞} -- 5.7 Characterization: the General Case -- 5.8 Wish List/Visualization -- 6 Groups of Möbius Transformations.
6.1 First Examples of Groups of Möbius Transformations -- 6.2 Fundamental Domains and Discrete Groups -- 6.3 Special Möbius Transformations -- 6.4 Digression: Hyperbolic Geometry -- 6.4.1 Hyperbolic Geometry I: The Upper Half-plane -- 6.4.2 Hyperbolic Geometry II: The Unit Circle -- 6.5 The Modular Group -- 6.6 Groups with Two Generators -- 6.7 Schottky Groups -- 6.8 The Mystery of the Parabolic Commutator -- 6.9 The Structure of Kleinian Groups -- 6.9.1 The Isometric Circles -- 6.9.2 The Limit Set -- 6.9.3 A Fundamental Domain -- 6.10 Parabolic Commutators: Construction -- References for Part II -- Part III Penrose Tilings -- 7 Penrose Tilings -- 7.1 Non-periodic Tilings: The Problem -- 7.2 The "Golden" Penrose Triangles -- 7.3 Which Tiling Patterns are Possible? -- 7.4 Index Sequences Generate Tilings -- 7.5 Isomorphisms of Penrose Tilings -- 7.6 Supplements -- References for Part III -- Index. |
| Record Nr. | UNINA-9910629301203321 |
|
Behrends Ehrhard <1946->
|
||
| Wiesbaden, Germany : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Tilings of the plane : from Escher via Möbius to Penrose / / Ehrhard Behrends
| Tilings of the plane : from Escher via Möbius to Penrose / / Ehrhard Behrends |
| Autore | Behrends Ehrhard <1946-> |
| Pubbl/distr/stampa | Wiesbaden, Germany : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (284 pages) |
| Disciplina | 516.132 |
| Collana | Mathematics study resources |
| Soggetto topico |
Tessellations (Mathematics)
Mosaics (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783658388102
9783658388096 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- Part I Looking over Escher's Shoulder -- 2 Symmetries and Fundamental Domains -- 2.1 What is Symmetry? -- 2.2 What Movements are There? -- 2.3 Groups of Movements -- 2.4 Discontinuous Groups and Fundamental Domains -- 3 The Discontinuous Symmetry Groups of the Plane -- 3.1 How Many Different Groups of Movements are There? -- 3.2 Finite Groups of Movements -- 3.3 The Subgroup of Translations -- 3.4 The 7 Frieze Groups -- 3.4.1 : Only Translations -- 3.4.2 : Only Reflections of Type 1 () -- 3.4.3 : Only Reflections of Type 2 () -- 3.4.4 : Proper Glide Reflections () -- 3.4.5 : Only Rotations () -- 3.4.6 : Rotations, Type-1 and Type-2 Reflections () -- 3.4.7 : Proper Glide Reflections, Type-2 Reflections, and Rotations () -- 3.4.8 Summary -- 3.4.9 Classification: A Test -- 3.4.10 Hints for Artists -- 3.5 The 17 Plane Crystal Groups -- 3.5.1 The Crystallographic Restriction -- 3.5.2 Translations, Reflections: 4 Groups -- 3.5.3 Translations, 2-Rotations, Reflections: 5 Groups -- 3.5.4 Translations, 3-Rotations, (Glide) Reflections: 3 Groups -- 3.5.5 Translations, 4-Rotations, Reflections: 3 Groups -- 3.5.6 Translations, 6-Rotations, Reflections: 2 Groups -- 3.5.7 Classification: A Test -- 4 The Heesch Constructions -- 4.1 Lattices and Nets -- 4.2 The Heesch Construction: Motivation -- 4.3 The Heesch Constructions: 28 Methods -- References for Part I -- Part II Möbius Transformations -- 5 Möbius Transformations -- 5.1 Complex Numbers: Some Reminders -- 5.2 Möbius Transformations: Definitions and First Results -- 5.3 Möbius Transformations and Circles -- 5.4 Fixed Points of Möbius Transformations -- 5.5 Conjugate Möbius Transformations -- 5.6 Characterization: Fixed Points in {0,∞} -- 5.7 Characterization: the General Case -- 5.8 Wish List/Visualization -- 6 Groups of Möbius Transformations.
6.1 First Examples of Groups of Möbius Transformations -- 6.2 Fundamental Domains and Discrete Groups -- 6.3 Special Möbius Transformations -- 6.4 Digression: Hyperbolic Geometry -- 6.4.1 Hyperbolic Geometry I: The Upper Half-plane -- 6.4.2 Hyperbolic Geometry II: The Unit Circle -- 6.5 The Modular Group -- 6.6 Groups with Two Generators -- 6.7 Schottky Groups -- 6.8 The Mystery of the Parabolic Commutator -- 6.9 The Structure of Kleinian Groups -- 6.9.1 The Isometric Circles -- 6.9.2 The Limit Set -- 6.9.3 A Fundamental Domain -- 6.10 Parabolic Commutators: Construction -- References for Part II -- Part III Penrose Tilings -- 7 Penrose Tilings -- 7.1 Non-periodic Tilings: The Problem -- 7.2 The "Golden" Penrose Triangles -- 7.3 Which Tiling Patterns are Possible? -- 7.4 Index Sequences Generate Tilings -- 7.5 Isomorphisms of Penrose Tilings -- 7.6 Supplements -- References for Part III -- Index. |
| Record Nr. | UNISA-996499870803316 |
|
Behrends Ehrhard <1946->
|
||
| Wiesbaden, Germany : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
