| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910964617603321 |
|
|
Autore |
Anderson James W |
|
|
Titolo |
Hyperbolic Geometry / / by James W. Anderson |
|
|
|
|
|
Pubbl/distr/stampa |
|
|
London : , : Springer London : , : Imprint : Springer, , 1999 |
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
Edizione |
[1st ed. 1999.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (IX, 230 p.) |
|
|
|
|
|
|
Collana |
|
Springer Undergraduate Mathematics Series, , 2197-4144 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Note generali |
|
|
|
|
|
|
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. . |
|
|
|
|
|
| |