# Geometry: A Comprehensive Course

Courier Corporation, Jan 1, 1988 - Mathematics - 449 pages
"A lucid and masterly survey." — Mathematics Gazette 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.

### Contents

 PRELIMINARY NOTIONS 1 VECTORS 20 CIRCLES 56 COAXAL SYSTEMS OF CIRCLES 106 THE REPRESENTATION OF CIRCLES BY POINTS IN SPACE OF THREE DIMENSIONS 126 MAPPINGS OF THE EUCLIDEAN PLANE 160
 MAPPINGS OF THE INVERSIVE PLANE 206 THE PROJECTIVE PLANE AND PROJECTIVE SPACE 242 THE PROJECTIVE GEOMETRY OF n DIMENSIONS 271 THE PROJECTIVE GENERATION OF CONICS AND QUADRICS 321 PRELUDE TO ALGEBRAIC GEOMETRY 401 Copyright