Hyperbolic Geometry

by Birger Iversen

Overview

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.

Product Details

ISBN-13:	9780521435284
Publisher:	Cambridge University Press
Publication date:	12/17/1992
Series:	London Mathematical Society Student Texts , #25
Edition description:	New Edition
Pages:	316
Product dimensions:	5.98(w) x 9.02(h) x 0.71(d)

Table of Contents

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.