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Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry

Geometry Illuminated: An Illustrated Introduction to Euclidean and Hyperbolic Plane Geometry

Matthew Harvey

Catalog Code: GIL
Print ISBN: 978-1-93951-211-6
Electronic ISBN: 978-1-61444-618-7
560 pp., Hardbound, 2015
List Price: $70.00
Member Price: $52.50
Series: MAA Textbooks

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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 Poincaré 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.

Table of Contents

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. Harvey graduated from the University of Virginia in 1995 with a B.A. in Mathematics, and from John Hopkins University in 2002 with a Ph.D in Mathematics.

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