Professor Pedoe is widely known as a fine teacher and a fine
geometer. His abilities in both areas are clearly evident in this
self-contained, well-written, and lucid introduction to the scope and
methods of elementary geometry. It covers the geometry usually included
in undergraduate courses in mathematics, except for the theory of convex
sets. Based on a course given by the author for several years at the
University of Minnesota, the main purpose of the book is to increase
geometrical, and therefore mathematical, understanding and to help
students enjoy geometry.
Among the topics discussed: the use
of vectors and their products in work on Desargues' and Pappus' theorem
and the nine-point circle; circles and coaxal systems; the
representation of circles by points in three dimensions; mappings of the
Euclidean plane, similitudes, isometries, mappings of the inversive
plane, and Moebius transformations; projective geometry of the plane,
space, and n dimensions; the projective generation of conics and
quadrics; Moebius tetrahedra; the tetrahedral complex; the twisted cubic
curve; the cubic surface; oriented circles; and introduction to
algebraic geometry.
In addition, three appendices deal with
Euclidean definitions, postulates, and propositions; the
Grassmann-Pluecker coordinates of lines in S3, and the group of circular
transformations. Among the outstanding features of this book are its
many worked examples and over 500 exercises to test geometrical
understanding.
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