Overview
- THIS IS THE FIRST GENUINELY INTRODUCTORY TEXTBOOK DEVOTED TO THE TOPIC: IT IS SELF-CONTAINED AND ASSUMES VERY FEW PREREQUISITES.
- INCLUDES FULL SOLUTIONS FOR ALL EXERCISES - THE ONLY BOOK ON THE SUBJECT TO DO SO.
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (6 chapters)
Keywords
About this book
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 new exercises.
Reviews
Praise for the first edition: "... The textbook is a good and useful introduction to hyperbolic geometry, and can be recommended for undergraduate courses."
Newsletter of the EMS, Issue 41, December 2001
From the reviews of the second edition:
"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." (L’Enseignement Mathematique, Vol. 51 (3-4), 2005)
Authors and Affiliations
Bibliographic Information
Book Title: Hyperbolic Geometry
Authors: James W. Anderson
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-1-4471-3987-4
Publisher: Springer London
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag London 1999
eBook ISBN: 978-1-4471-3987-4Published: 29 June 2013
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: IX, 230
Number of Illustrations: 15 b/w illustrations
Topics: Geometry, Mathematics, general