03720nam 22006735 450 991030012730332120200705200717.03-319-74135-710.1007/978-3-319-74135-2(CKB)4100000002892300(DE-He213)978-3-319-74135-2(MiAaPQ)EBC5588822(MiAaPQ)EBC6314652(Au-PeEL)EBL5588822(OCoLC)1029870899(PPN)225553503(EXLCZ)99410000000289230020180321d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierGeometry Through History[electronic resource] Euclidean, Hyperbolic, and Projective Geometries /by Meighan I. Dillon1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XII, 350 p. 233 illus. in color.) 3-319-74134-9 Preface -- 1. The Elements of Euclid -- 2. Neutral Geometry -- 3. The Hyperbolic Plane -- 4. Hilbert's Grundlagen -- 5. More Euclidean Geometry -- 6. Models for the Hyperbolic Plane -- 7. Affine Geometry -- 8. An Introduction to Projective Geometry -- 9. Algebraic Curves -- 10. Rotations and Quaternions -- Index.Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.Convex geometry Discrete geometryMathematicsHistoryHyperbolic geometryProjective geometryConvex and Discrete Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21014History of Mathematical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M23009Hyperbolic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21030Projective Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21050Convex geometry .Discrete geometry.Mathematics.History.Hyperbolic geometry.Projective geometry.Convex and Discrete Geometry.History of Mathematical Sciences.Hyperbolic Geometry.Projective Geometry.519.009Dillon Meighan Iauthttp://id.loc.gov/vocabulary/relators/aut888238MiAaPQMiAaPQMiAaPQBOOK9910300127303321Geometry Through History1984168UNINA