
Accession Number : AD0720779
Title : Incidence Axioms for Affine Geometry,
Corporate Author : CALIFORNIA INST OF TECH PASADENA
Personal Author(s) : Hall,Marshall , Jr
Report Date : 1971
Pagination or Media Count : 23
Abstract : In terms of incidence alone it is possible to define an affine plane, as Artin does, by calling lines parallel if they do not intersect, and basing the definition on the Euclidean axiom that there is a unique parallel to a line through a point not on the line. In higher dimensions one can define affine geometry by deleting the points and lines of a hyperplane from a projective geometry, using the axioms of Veblen and Young. It is an easy exercise to show that the Artin approach and that of Veblen and Young agree in the definition of an affine plane. But in higher dimensions it is not clear how an affine geometry can be defined directly so that it can be shown to arise from a projective geometry by deleting the points and lines of a hyperplane. This paper gives a set of axioms which have this property. (Author)
Descriptors : (*PROJECTIVE GEOMETRY, THEOREMS), GROUPS(MATHEMATICS), PERMUTATIONS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE