Fundamental Concepts of Geometry

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Courier Dover Publications, 1983 - Mathematics - 321 pages
2 Reviews

Fundamental Concepts of Geometry demonstrates in a clear and lucid manner the relationships of several types of geometry to one another. This highly regarded work is a superior teaching text, especially valuable in teacher preparation, as well as providing an excellent overview of the foundations and historical evolution of geometrical concepts.
Professor Meserve (University of Vermont) offers students and prospective teachers the broad mathematical perspective gained from an elementary treatment of the fundamental concepts of mathematics. The clearly presented text is written on an undergraduate (or advanced secondary-school) level and includes numerous exercises and a brief bibliography. An indispensable taddition to any math library, this helpful guide will enable the reader to discover the relationships among Euclidean plane geometry and other geometries; obtain a practical understanding of "proof"; view geometry as a logical system based on postulates and undefined elements; and appreciate the historical evolution of geometric concepts.

  

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Contents

FOUNDATIONS OF GEOMETRY
1
SYNTHETIC PROJECTIVE GEOMETRY
25
COORDINATE SYSTEMS
69
ANALYTIC PROJECTIVE GEOMETRY
103
AFFINE GEOMETRY
150
EUCLIDEAN PLANE GEOMETRY
185
THE EVOLUTION OF GEOMETRY
219
NONEUCLIDEAN GEOMETRY
268
TOPOLOGY
288
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