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)
Hyperbolic Geometry
von James W. AndersonThe 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.
