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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