TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Hyperbolic Geometry
T2  - Springer Undergraduate Mathematics Series,
SN  - 9781846282201
AV  - QA440-699 
U1  - 516 23
PY  - 2005///
CY  - London
PB  - Springer London
KW  - Mathematics
KW  - Geometry
KW  - Mathematics, general
N1  - The Basic Spaces -- The General Mȵbius Group -- Length and Distance in ? -- Planar Models of the Hyperbolic Plane -- Convexity, Area, and Trigonometry -- Nonplanar models; ZDB-2-SMA
N2  - 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, Mȵbius transformations, the general Mȵbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the PoincarȨ 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
UR  - http://dx.doi.org/10.1007/1-84628-220-9
ER  -