Geometry: A Comprehensive Course (for Mathematics Enthusiasts)

A Lucid and Masterly Survey

Professor Pedoe is widely known as both a fine teacher and a fine geometer. This self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry clearly exhibits his abilities in both areas. The book 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.

The topics discussed in the book include 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 an introduction to algebraic geometry.

Additionally, the book includes three appendices that deal with Euclidean definitions, postulates, and propositions; the Grassmann-Pluecker coordinates of lines in S3; and the group of circular transformations. One of the outstanding features of this book is its abundance of worked examples and over 500 exercises to test geometrical understanding.

This "Mathematics Gazette" review succinctly captures the essence of Professor Pedoe's work, describing it as a "lucid and masterly survey" that showcases the author's exceptional teaching and geometric abilities. The book's comprehensive coverage of elementary geometry, its clear and accessible presentation, and its wealth of practical applications and exercises make it an invaluable resource for both students and mathematicians alike.

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