Hyperbolic Geometry

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

Birger Iversen (Author)

9780521435284, Cambridge University Press

Paperback, published 17 December 1992

316 pages
22.9 x 15.2 x 1.8 cm, 0.46 kg

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.

Introduction
1. Quadratic Forms
2. Geometries
3. Hyperbolic Plane
4. Fuchsian Groups
5. Fundamental Domains
6. Coverings
7. Poincare's Theorem
8. Hyperbolic 3-Space
Appendix: Axioms for Plane Geometry.

Subject Areas: Geometry [PBM]