Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks) - Hardcover
Synopsis
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.
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About the Author
Matthew Harvey is an Associate Professor of Mathematics at the University of Virginia's College at Wise, where he has taught since 2006. He graduated from the University of Virginia in 1995 with a BA in Mathematics, and from Johns Hopkins University in 2002 with a PhD in Mathematics.
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Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (MAA Textbooks)
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American Mathematical Society, 2015
ISBN 10: 1939512115
ISBN 13: 9781939512116
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Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry (Mathematical Association of America Textbooks)
Published by
American Mathematical Society, 2015
ISBN 10: 1939512115
ISBN 13: 9781939512116
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Geometry Illuminated - An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry
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Geometry Illuminated An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry
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Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry
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ISBN 10: 1939512115
ISBN 13: 9781939512116
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Geometry Illuminated
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Condition: New. Über den AutorrnrnMatthew Harvey is an Associate Professor of Mathematics at the University of Virginia s College at Wise, where he has taught since 2006. He graduated from the University of Virginia in 1995 with a BA in Mathematics, and fr. Seller Inventory # 107270623
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Geometry Illuminated : An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry
Published by
Mathematical Association Of America (MAA) Sep 2015, 2015
ISBN 10: 1939512115
ISBN 13: 9781939512116
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Buch. Condition: Neu. Neuware - Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very 'visual' subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides.Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincar disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings. Seller Inventory # 9781939512116
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