{"product_id":"geometries-9780821875711","title":"Geometries","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal - although some remain more equal than others.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e[A] very ambitious and pleasantly succinct text . . . Highly recommended.\" - \u003cem\u003eCHOICE\u003c\/em\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003ePreface\u003c\/li\u003e\n\u003cli\u003eAbout Euclidean geometry\u003c\/li\u003e\n\u003cli\u003eToy geometries and main definitions\u003c\/li\u003e\n\u003cli\u003eAbstract groups and group presentations\u003c\/li\u003e\n\u003cli\u003eFinite subgroups of 𝑆𝑂(3) and the platonic bodies\u003c\/li\u003e\n\u003cli\u003eDiscrete subgroups of the isometry group of the plane and tilings\u003c\/li\u003e\n\u003cli\u003eReflection groups and Coxeter geometries\u003c\/li\u003e\n\u003cli\u003eSpherical geometry\u003c\/li\u003e\n\u003cli\u003eThe Poincaré disk model of hyperbolic geometry\u003c\/li\u003e\n\u003cli\u003eThe Poincaré half-plane model\u003c\/li\u003e\n\u003cli\u003eThe Cayley-Klein model\u003c\/li\u003e\n\u003cli\u003eHyperbolic trigonometry and absolute constants\u003c\/li\u003e\n\u003cli\u003eHistory of non-Euclidean geometry\u003c\/li\u003e\n\u003cli\u003eProjective geometry\u003c\/li\u003e\n\u003cli\u003e“Projective geometry is all geometry”\u003c\/li\u003e\n\u003cli\u003eFinite geometries\u003c\/li\u003e\n\u003cli\u003eThe hierarchy of geometries\u003c\/li\u003e\n\u003cli\u003eMorphisms of geometries\u003c\/li\u003e\n\u003cli\u003eExcerpts from Euclid’s “Elements”\u003c\/li\u003e\n\u003cli\u003eHilbert’s axioms for plane geometry\u003c\/li\u003e\n\u003cli\u003eAnswers \u0026amp; hints\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50577675780439,"sku":"9780821875711","price":46.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780821875711.jpg?v=1746096124","url":"https:\/\/bookcurl.com\/products\/geometries-9780821875711","provider":"Book Curl","version":"1.0","type":"link"}