03369nam 22006015 450 991096461760332120250730104846.01-4471-3987-910.1007/978-1-4471-3987-4(CKB)2660000000025486(SSID)ssj0000914890(PQKBManifestationID)11508792(PQKBTitleCode)TC0000914890(PQKBWorkID)10864523(PQKB)10759758(DE-He213)978-1-4471-3987-4(MiAaPQ)EBC3073446(PPN)23799397X(EXLCZ)99266000000002548620130522d1999 u| 0engurnn|008mamaatxtccrHyperbolic Geometry /by James W. Anderson1st ed. 1999.London :Springer London :Imprint: Springer,1999.1 online resource (IX, 230 p.) Springer Undergraduate Mathematics Series,2197-4144"With 20 Figures."1-85233-156-9 Includes bibliographical references and index.1. The Basic Spaces -- 2. The General Möbius 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.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. .Springer Undergraduate Mathematics Series,2197-4144GeometryMathematicsGeometryMathematicsGeometry.Mathematics.Geometry.Mathematics.516.9Anderson James Wauthttp://id.loc.gov/vocabulary/relators/aut164195MiAaPQMiAaPQMiAaPQBOOK9910964617603321Hyperbolic geometry1427625UNINA