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Continuous Symmetry: From Euclid to Klein
William Barker, Bowdoin College, Brunswick, ME, and Roger Howe, Yale University, New Haven, CT
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2007; 544 pp; hardcover
ISBN-10: 0-8218-3900-4
ISBN-13: 978-0-8218-3900-3
List Price: US$71
Member Price: US$56.80
Order Code: MBK/47
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The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry.

The primary focus of the book is on transformations of the plane. The transformational point of view provides both a path for deeper understanding of traditional synthetic geometry and tools for providing proofs that spring from a consistent point of view. As a result, proofs become more comprehensible, as techniques can be used and reused in similar settings.

The approach to the material is very concrete, with complete explanations of all the important ideas, including foundational background. The discussions of the nine-point circle and wallpaper groups are particular examples of how the strength of the transformational point of view and the care of the authors' exposition combine to give a remarkable presentation of topics in geometry.

This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises.

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Readership

Undergraduates interested in geometry.

Reviews

"All in all, this is a very nice book (that is) worth reading... It should be in every library, and (would) be useful to students and teachers alike."

-- Mathematical Reviews

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