Hyperbolic Geometry
(Springer Undergraduate Mathematics Series)
| データ種別 | 電子ブック |
|---|---|
| 版 | Second Edition |
| 出版者 | London : Springer London |
| 出版年 | 2005 |
| 本文言語 | 英語 |
| 大きさ | XII, 276 p. 21 illus : online resource |
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| 内容注記 | The Basic Spaces The General Möbius Group Length and Distance in ? Planar Models of the Hyperbolic Plane Convexity, Area, and Trigonometry Nonplanar models |
|---|---|
| 一般注記 | 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. |
| 著者標目 | SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Geometry FREE:Mathematics FREE:Geometry FREE:Mathematics, general |
| 分 類 | DC23:516 |
| 巻冊次 | ISBN:9781846282201 
|
| ISBN | 9781846282201 |
| URL | http://dx.doi.org/10.1007/1-84628-220-9 |
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