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harvey m geometry illuminated illustrated introduction 2015

Type:: E-books
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Textbook in PDF format An 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. -- Provided by publisher. Axioms and models Neutral Geometry The axioms of incidence and order Angles and triangles Congruence verse I: SAS and ASA Congruence verse II: AAS Congruence verse III: SSS Distance, length and the axioms of continuity Angle measure Triangles in neutral geometry Polygons Quadrilateral congruence theorems Euclidean Geometry The axiom on parallels Parallel projection Similarity Circles Circumference Euclidean constructions Concurrence I Concurrence II Concurrence III Trilinear coordinates Euclidean Transformations Analytic geometry Isometries Reflections Translations and rotations Orientation Glide reflections Change of coordinates Dilation Applications of transformations Area I Area II Barycentric coordinates Inversion I Inversion II Applications of inversion Hyperbolic Geometry The search for a rectangle Non-Euclidean parallels The pseudosphere Geodesics on the pseudosphere The upper half-plane The Poincaré disk Hyperbolic reflections Orientation preserving hyperbolic isometries The six hyperbolic trigonometric functions Hyperbolic trigonometry Hyperbolic area Tiling

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Harvey M. Geometry Illuminated. An Illustrated Introduction...2015.pdf 37.0 MB

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harvey m geometry illuminated illustrated introduction 2015

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