Continuous Symmetry

Continuous Symmetry

Review[C]areful, rigorous, thorough and explicit in its attention to detail.... [A] fine introduction to the habits of logical thinking and precise exposition.... [T]he material is arranged in a manner that invites and inspires one to reflect about the connections among the ideas being discussed. It is thought provoking throughout. -- MAA Reviews"[The basic results on rigid motions are] done in excellent detail with examples and diagrams for the reader.... [N]ice applications of the group-theoretic point of view to more advanced results of Euclidean geometry. ... [T]his is a substantial book with a lot of good material in it, well worth studying." - MAA MonthlyThe 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.