Hyperbolic Geometry

2. Auflage 2005
ISBN: 978-1-85233-934-0
Verlag: Springer Us

Buch, Englisch, 276 Seiten, Format (B × H): 251 mm x 174 mm, Gewicht: 1130 g

Reihe: Springer Undergraduate Mathematics Series

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Anderson, James W

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

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