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AuthorAnderson, James W. author
TitleHyperbolic Geometry [electronic resource] / by James W. Anderson
ImprintLondon : Springer London : Imprint: Springer, 1999
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Descript IX, 230 p. online resource


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, Mรถbius transformations, the general Mรถbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincarรฉ 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.


1. The Basic Spaces -- 2. The General Mรถbius Group -- 3. Length and Distance in ? -- 4. Other Models of the Hyperbolic Plane -- 5. Convexity, Area, and Trigonometry -- 6. Groups Acting on ? -- Solutions -- Further Reading -- References -- Notation

Mathematics Geometry Mathematics Geometry Mathematics general


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