Hyperbolic Geometry / Edition 2

by James W. Anderson

Overview

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, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon 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;
• a brief discussion of generalizations to higher dimensions;
• many newexercises.

Product Details

ISBN-13:	9781852339340
Publisher:	Springer London
Publication date:	08/02/2005
Series:	Springer Undergraduate Mathematics Series
Edition description:	2nd ed. 2005
Pages:	276
Product dimensions:	7.01(w) x 10.00(h) x 0.02(d)

Table of Contents

The Basic Spaces.- The General Möbius Group.- Length and Distance in—.- Planar Models of the Hyperbolic Plane.- Convexity, Area, and Trigonometry.- Nonplanar models.