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Geometry: A Comprehensive Course
"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.
Reprint of A Course for Geometry for Colleges and Universities, Cambridge University Press, Cambridge, England, 1970.
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"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.
Reprint of A Course for Geometry for Colleges and Universities, Cambridge University Press, Cambridge, England, 1970.
algebraic geometry;projective geometry;geometry class;education majors;graph theory;abstract algebra;primitive roots;math textbook;theory class;euclidean geometry;advanced study;advanced concepts;pure mathematics;linear algebra;mathematical background;upper half;math major;wait awhile;pleasant memories;odd times;liberal arts;mappings;coxeter;combinatorial;combinatorics;one-semester;quadratic;brannan;topological;partitions;non-euclidean;mendelson;self-study;moebius;euclid;poincare;topology;axiomatic;wylie;theorems;arithmetic;terseness;analytic;metric;calculus;generating;proofs;fundamentals;transformations;graphs;revisited;spaces;cited;definitions;introductory;exercises;books on projective geometries;books on arithmetics;books on geometry classes;books on combinatorics;books on advanced concepts;waiting awhile;books on theorems;books on mendelson;books on advanced studies;books on brannan;books on linear algebras;books on pure mathematics;books on upper halves;books on math majors;books on proofs;books on mappings;books on odd times;books on topologies;books on partitions;books on calculus;books on fundamentals;books on coxeters;books on poincare;books on theory classes;books on euclidean geometries;books on abstract algebras;books on algebraic geometries;books on moebius;books on graph theories;books on euclids;books on graphs;books on transformations;books on wylie;books on education majors;books on self-studies;books on math textbooks;books on liberal arts;books on spaces
