Fundamental Concepts of Geometry

Front Cover
Courier Corporation, Dec 8, 2014 - Mathematics - 336 pages

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.

 

Selected pages

Contents

FOUNDATIONS OF GEOMETRY
7
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
Copyright

Other editions - View all

Fundamental Concepts of Geometry
Bruce Elwyn Meserve
Snippet view - 1955
Fundamental Concepts of Geometry
Bruce Elwyn Meserve
Snippet view - 1955
Fundamental Concepts of Geometry
Bruce Elwyn Meserve
Snippet view - 1953
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Common terms and phrases

absolute involution affine geometry affine transformation algebraic analytic projective geometry called century collinear complete quadrangle concepts conic considered construction coordinate system coplanar cross ratio defined definitions determined diagonal directed angle elements elliptic geometry equation equiareal transformation equivalent Euclid's euclidean geometry euclidean transformations exists fifth postulate harmonic sets homeomorphic homogeneous coordinates homothetic transformation hyperbolic geometry hyperbolic line ideal line ideal point identity transformation integer intersect invariant points involution isomorphic line segment mathematical matrix mid-point noneuclidean geometries nonhomogeneous coordinates obtained ordinary points orthogonal line reflections parallel pencil of lines pencil of points perpendicular perspective plane dual point reflection points and lines polarity Postulates P-1 projective transformation proof properties Prove quadrangular set quadrilateral rational real numbers real projective plane Repeat Exercise right angles rotation set of points set of postulates sides similarity transformations statement surface synthetic projective geometry Theorem three distinct points three-space tion topology trans triples undefined vertices

Bibliographic information

TitleFundamental Concepts of Geometry
Dover Books on Mathematics
AuthorBruce E. Meserve
Editionreprint, revised
PublisherCourier Corporation, 2014
ISBN048615226X, 9780486152264
Length336 pages
Subjects ›  › 

Mathematics / Geometry / General
  
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