{"product_id":"hyperbolic-geometry-9781852339340","title":"Hyperbolic Geometry","description":"\u003cp\u003e • Author(s): James W. Anderson\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Geometry - Non-Euclidean\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\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","brand":"Springer","offers":[{"title":"Paperback","offer_id":45275178533015,"sku":"9781852339340","price":2543.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781852339340.webp?v=1769282127","url":"https:\/\/atlanticbooks.com\/products\/hyperbolic-geometry-9781852339340","provider":"Atlantic Books","version":"1.0","type":"link"}