Hyperbolic Geometry
Seiten
2000
Springer London Ltd (Verlag)
978-1-85233-156-6 (ISBN)
Springer London Ltd (Verlag)
978-1-85233-156-6 (ISBN)
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This introductory text explores and develops the basic notions of geometry on the hyperbolic plane. 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 and more.
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.
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.
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
| Reihe/Serie | Springer Undergraduate Mathematics Series |
|---|---|
| Zusatzinfo | 20 figs. |
| Verlagsort | England |
| Sprache | englisch |
| Einbandart | Paperback |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-85233-156-9 / 1852331569 |
| ISBN-13 | 978-1-85233-156-6 / 9781852331566 |
| Zustand | Neuware |
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