Home / Science / Mathematics / Geometry / Hyperbolic Geometry

Hyperbolic Geometry

Upon request
Dispatched within 10 - 15 working days. Ρrovided that there's sufficient stock at the supplier.

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, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula 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;

- brief discussion of generalizations to higher dimensions;

- many new exercises.

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.

Author: Anderson James
Publisher: SPRINGER
Pages: 276
ISBN: 9781852339340
Cover: Paperback
Edition Number: 2
Release Year: 2005

You may also like


Subscribe to the newsletter to be the first to receive our new releases and offers
Your account