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[null,"1.","Record Nr.",null,"UNINA9910964617603321"]
[null,null,"Autore",null,"Anderson James W"]
[null,null,"Titolo",null,"Hyperbolic Geometry / / by James W. Anderson"]
[null,null,"Pubbl/distr/stampa",null,"London : , : Springer London : , : Imprint : Springer, , 1999"]
[null,null,"ISBN",null,"1-4471-3987-9"]
[null,null,"Edizione",null,"[1st ed. 1999.]"]
[null,null,"Descrizione fisica",null,"1 online resource (IX, 230 p.)"]
[null,null,"Collana",null,"Springer Undergraduate Mathematics Series, , 2197-4144"]
[null,null,"Disciplina",null,"516.9"]
[null,null,"Soggetti",null,"Geometry"]
[{"$nulls":4},"Mathematics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","\"With 20 Figures.\""]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"Sommario/riassunto","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. ."]