Hyperbolic Geometry / / by James W. Anderson
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| Autore: |
Anderson James W
|
| Titolo: |
Hyperbolic Geometry / / by James W. Anderson
|
| Pubblicazione: | London : , : Springer London : , : Imprint : Springer, , 1999 |
| Edizione: | 1st ed. 1999. |
| Descrizione fisica: | 1 online resource (IX, 230 p.) |
| Disciplina: | 516.9 |
| Soggetto topico: | Geometry |
| Mathematics | |
| Note generali: | "With 20 Figures." |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 1. The Basic Spaces -- 2. The General Möbius Group -- 3. Length and Distance in ? -- 4. Other Models of the Hyperbolic Plane -- 5. Convexity, Area, and Trigonometry -- 6. Groups Acting on ? -- Solutions -- Further Reading -- References -- Notation. |
| Sommario/riassunto: | The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications. This updated second edition also features: an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; the hyperboloid model of the hyperbolic plane; brief discussion of generalizations to higher dimensions; many new exercises. The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape. . |
| Titolo autorizzato: | Hyperbolic geometry |
| ISBN: | 1-4471-3987-9 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910964617603321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Springer Undergraduate Mathematics Series, . 2197-4144