{"product_id":"hyperbolic-geometry-paperback","title":"Hyperbolic Geometry - Paperback","description":"\u003cp\u003eby \u003cb\u003eJames W. Anderson\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis introductory text explores and develops the basic notions of geometry on the hyperbolic plane. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincar disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications. Coverage provides readers with a firm grasp of the concepts and techniques of this beautiful area of mathematics.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eTopics 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.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThis updated second edition also features: \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003ean expanded discussion of planar models of the hyperbolic plane arising from complex analysis; \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003ethe hyperboloid model of the hyperbolic plane; \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003ebrief discussion of generalizations to higher dimensions; \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003emany new exercises. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 276\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.7 x 9.9 x 6.9 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e August 23, 2005\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42742119661631,"sku":"9781852339340","price":73.85,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/5840b9f6b093656286012ad0e9214379.webp?v=1765162776","url":"https:\/\/dhlswag.com\/products\/hyperbolic-geometry-paperback","provider":"BBB","version":"1.0","type":"link"}