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 Poincare disk model.

An extensively illustrated introduction to Euclidean and hyperbolic geometry in the plane, designed for undergraduate courses in geometry.

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.

Reviews
...The author succeeds in elevating Euclidean geometry in particular to the level of advanced undergraduate study and in so doing presents it as a counterpart to a first analysis course. At the same time, some readers may prefer to move on to new ideas and results more quickly; to that end, Harvey gives an indication of several paths through the book in his preface." - Choice

"To my mind, this book stands out from the crowd partly because of the way in which its imaginatively devised illustrations are used to stage the introduction of basic concepts and to guide the reader through various steps in a proof. It's not just a matter of pretty pictures, however, because Matthew Harvey's written commentary is easy going and yet mathematically precise. He has written a truly lovely book, which is now top of my reading list as an introduction to geometry at this level." - Peter Ruane



Book Information
ISBN 9781939512116
Author Matthew Harvey
Format Hardback
Page Count 558
Imprint Mathematical Association of America
Publisher Mathematical Association of America
Weight(grams) 1150g
Dimensions(mm) 262mm * 185mm * 32mm