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Continuous Symmetry
William H. Barker
Roger Howe
其他書名
From Euclid to Klein
出版
American Mathematical Soc.
, 2007
主題
Mathematics / Geometry / General
Mathematics / Group Theory
ISBN
0821839004
9780821839003
URL
http://books.google.com.hk/books?id=88EjDwAAQBAJ&hl=&source=gbs_api
EBook
SAMPLE
註釋
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.