{"product_id":"9780883856482-geometric-transformations-iv","title":"Geometric Transformations IV","description":"\u003cmeta content=\"text\/html; charset=utf-8\" http-equiv=\"Content-Type\"\u003e\u003cp\u003e\u003cspan\u003eCircular Transformations\u003cbr\u003eThe familiar plane geometry of high school figures composed of lines and circles takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries.\u003cbr\u003eThe familiar plane geometry of high school figures composed of lines and circles takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries.\u003cbr\u003e\u003cbr\u003eThis book is the concluding Part IV of \u003cem\u003eGeometric Transformations\u003c\/em\u003e, but it can be studied independently of Parts I, II, and III, which appeared in this series as Volumes 8, 21, and 24. Part I treats the geometry of rigid motions of the plane (isometries); Part II treats the geometry of shape-preserving transformations of the plane (similarities); Part III treats the geometry of transformations of the plane that map lines to lines (affine and projective transformations) and introduces the Klein model of non-Euclidean geometry. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincar model of hyperbolic geometry.\u003cbr\u003e\u003cbr\u003eThe straightforward, direct presentation assumes only some background in high-school geometry and trigonometry. Numerous exercises lead the reader to a mastery of the methods and concepts. The second half of the book contains detailed solutions of all the problems.\u003cbr\u003e\u003cbr\u003e\u003c\/span\u003e\u003c\/p\u003e","brand":"Rarewaves","offers":[{"title":"Default Title","offer_id":58429642146166,"sku":"9780883856482","price":53.87,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0092\/7504\/8033\/files\/orig_38129074.jpg?v=1786371603","url":"https:\/\/www.rarewaves.com\/products\/9780883856482-geometric-transformations-iv","provider":"Rarewaves.com","version":"1.0","type":"link"}