Continuous symmetry: from Euclid to Klein

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