Hyperbolic geometry
著者
書誌事項
Hyperbolic geometry
（Springer undergraduate mathematics series）
Springer-Verlag, c1999
- : pbk
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注記
Includes bibliographical references (p. 223-224) and index
内容説明・目次
内容説明
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, taking the approach that hyperbolic geometry consists of the study of those quantities invariant under the action of a natural group of transformations. Topics covered include the upper half-space model of the hyperbolic plane, Mobius transformations, the general Mobius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincare disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications. The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics.
目次
- Preamble
- The Basic Spaces
- The General Mobius Group
- Length and Distance in H
- Other Models of the Hyperbolic Plane
- Convexity, Area and Trigonometry
- Groups acting on H
- Solutions
- Further Reading
- References
- Notation
- Index
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