Hyperbolic Geometry / Edition 1

Hyperbolic Geometry / Edition 1

by James W. Anderson
     
 

ISBN-10: 1852331569

ISBN-13: 9781852331566

Pub. Date: 10/28/1999

Publisher: Springer-Verlag New York, LLC

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, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving…  See more details below

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, suitable for third or fourth year undergraduates. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations.

Topics covered include the upper half-plane model of the hyperbolic plane, Mobius transformations, the general Mobius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincare disc model, convex subsets of the hyperbolic plane, the hyperbolic area, and the Gauss-Bonnet formula and its applications.

The style and level of the book, which assumes few mathematical prerequisites, make it an ideal introduction to this subject and provides the reader with a firm grasp of the concepts and techniques of this beautiful part of the mathematical landscape.

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Product Details

ISBN-13:
9781852331566
Publisher:
Springer-Verlag New York, LLC
Publication date:
10/28/1999
Series:
Undergraduate Mathematics Series
Edition description:
Older Edition
Pages:
248
Product dimensions:
6.70(w) x 9.22(h) x 0.59(d)

Table of Contents

1The basic spaces1
2The general Mobius group23
3Length and distance in H73
4Planar models of the hyperbolic plane117
5Convexity, area, and trigonometry145
6Nonplanar models189

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