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Hyperbolic Geometry
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 hyperboli...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Springer London : Imprint: Springer,
2005.
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| Edición: | 2nd ed. 2005. |
| Colección: | Springer Undergraduate Mathematics Series,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 100 | 1 | |a Anderson, James W. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Hyperbolic Geometry |h [electronic resource] / |c by James W. Anderson. |
| 250 | |a 2nd ed. 2005. | ||
| 264 | 1 | |a London : |b Springer London : |b Imprint: Springer, |c 2005. | |
| 300 | |a XII, 276 p. 21 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Springer Undergraduate Mathematics Series, |x 2197-4144 | |
| 505 | 0 | |a The Basic Spaces -- The General Möbius Group -- Length and Distance in ? -- Planar Models of the Hyperbolic Plane -- Convexity, Area, and Trigonometry -- Nonplanar models. | |
| 520 | |a 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. . | ||
| 650 | 0 | |a Geometry. | |
| 650 | 0 | |a Mathematics. | |
| 650 | 1 | 4 | |a Geometry. |
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| 776 | 0 | 8 | |i Printed edition: |z 9781852339340 |
| 830 | 0 | |a Springer Undergraduate Mathematics Series, |x 2197-4144 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/1-84628-220-9 |z Texto Completo |
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