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- catalog abstract "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, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré 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.".
- catalog contributor b11553600.
- catalog created "c1999.".
- catalog date "1999".
- catalog date "c1999.".
- catalog dateCopyrighted "c1999.".
- catalog description "1. The Basic Spaces -- 2. The General Mobius Group -- 3. Length and Distance in H -- 4. Other Models of the Hyperbolic Plane -- 5. Convexity, Area, and Trigonometry -- 6. Groups Acting on H.".
- catalog description "Includes bibliographical references (p. 221-224) and index.".
- catalog description "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, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré 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.".
- catalog extent "ix, 230 p. :".
- catalog hasFormat "Hyperbolic geometry.".
- catalog identifier "1852331569 (alk. paper)".
- catalog isFormatOf "Hyperbolic geometry.".
- catalog isPartOf "Springer undergraduate mathematics series".
- catalog issued "1999".
- catalog issued "c1999.".
- catalog language "eng".
- catalog publisher "London ; New York : Springer,".
- catalog relation "Hyperbolic geometry.".
- catalog subject "516.9 21".
- catalog subject "Geometry, Hyperbolic.".
- catalog subject "Geometry.".
- catalog subject "Mathematics.".
- catalog subject "QA685 .A54 1999".
- catalog tableOfContents "1. The Basic Spaces -- 2. The General Mobius Group -- 3. Length and Distance in H -- 4. Other Models of the Hyperbolic Plane -- 5. Convexity, Area, and Trigonometry -- 6. Groups Acting on H.".
- catalog title "Hyperbolic geometry / James W. Anderson.".
- catalog type "text".