{"product_id":"geometry-illuminated-an-illustrated-introduction-to-euclidean-and-hyperbolic-plane-geometry-hardback-9781939512116","title":"Geometry Illuminated; An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Hardback) 9781939512116","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eGeometry Illuminated\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eAn extensively illustrated introduction to Euclidean and hyperbolic geometry in the plane, designed for undergraduate courses in geometry.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMatthew Harvey (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781939512116, The Mathematical Association of America\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 September 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e558 pages\u003cbr\u003e26.2 x 18.5 x 3.2 cm, 1.15 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eAn introduction to geometry in the plane, both Euclidean and hyperbolic, this book is designed for an undergraduate course in geometry. With its patient approach, and plentiful illustrations, it will also be a stimulating read for anyone comfortable with the language of mathematical proof. While the material within is classical, it brings together topics that are not generally found together in books at this level, such as: parametric equations for the pseudosphere and its geodesics; trilinear and barycentric coordinates; Euclidean and hyperbolic tilings; and theorems proved using inversion. The book is divided into four parts, and begins by developing neutral geometry in the spirit of Hilbert, leading to the Saccheri–Legendre Theorem. Subsequent sections explore classical Euclidean geometry, with an emphasis on concurrence results, followed by transformations in the Euclidean plane, and the geometry of the Poincaré disk model.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eAxioms and models\u003cbr\u003e Part I. Neutral Geometry: 1. The axioms of incidence and order\u003cbr\u003e 2. Angles and triangles\u003cbr\u003e 3. Congruence verse I: SAS and ASA\u003cbr\u003e 4. Congruence verse II: AAS\u003cbr\u003e 5. Congruence verse III: SSS\u003cbr\u003e 6. Distance, length and the axioms of continuity\u003cbr\u003e 7. Angle measure\u003cbr\u003e 8. Triangles in neutral geometry\u003cbr\u003e 9. Polygons\u003cbr\u003e 10. Quadrilateral congruence theorems\u003cbr\u003e Part II. Euclidean Geometry: 11. The axiom on parallels\u003cbr\u003e 12. Parallel projection\u003cbr\u003e 13. Similarity\u003cbr\u003e 14. Circles\u003cbr\u003e 15. Circumference\u003cbr\u003e 16. Euclidean constructions\u003cbr\u003e 17. Concurrence I\u003cbr\u003e 18. Concurrence II\u003cbr\u003e 19. Concurrence III\u003cbr\u003e 20. Trilinear coordinates\u003cbr\u003e Part III. Euclidean Transformations: 21. Analytic geometry\u003cbr\u003e 22. Isometries\u003cbr\u003e 23. Reflections\u003cbr\u003e 24. Translations and rotations\u003cbr\u003e 25. Orientation\u003cbr\u003e 26. Glide reflections\u003cbr\u003e 27. Change of coordinates\u003cbr\u003e 28. Dilation\u003cbr\u003e 29. Applications of transformations\u003cbr\u003e 30. Area I\u003cbr\u003e 31. Area II\u003cbr\u003e 32. Barycentric coordinates\u003cbr\u003e 33. Inversion I\u003cbr\u003e 34. Inversion II\u003cbr\u003e 35. Applications of inversion\u003cbr\u003e Part IV. Hyperbolic Geometry: 36. The search for a rectangle\u003cbr\u003e 37. Non-Euclidean parallels\u003cbr\u003e 38. The pseudosphere\u003cbr\u003e 39. Geodesics on the pseudosphere\u003cbr\u003e 40. The upper half-plane\u003cbr\u003e 41. The Poincaré disk\u003cbr\u003e 42. Hyperbolic reflections\u003cbr\u003e 43. Orientation preserving hyperbolic isometries\u003cbr\u003e 44. The six hyperbolic trigonometric functions\u003cbr\u003e 45. Hyperbolic trigonometry\u003cbr\u003e 46. Hyperbolic area\u003cbr\u003e 47. Tiling\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Euclidean geometry [\u003ca title=\"See our other books on Euclidean geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Euclidean%20geometry%20%5BPBMH%5D%22\"\u003ePBMH\u003c\/a\u003e], Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"The Mathematical Association of America","offers":[{"title":"Brand New","offer_id":52449446068504,"sku":"9781939512116","price":46.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781939512116i.jpg?v=1785199623","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/geometry-illuminated-an-illustrated-introduction-to-euclidean-and-hyperbolic-plane-geometry-hardback-9781939512116","provider":"Freshly Printed Books","version":"1.0","type":"link"}