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Definition of Affine Geometry by a Group of Transformations

Published online by Cambridge University Press:  20 November 2018

Joe Lipman
Joe Lipman*
Affiliation:
Summer Research Institute, Queen's University
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In his Geometric Algebra (New York, 1957) E. Artin poses the problem of co-ordinatizing an affine plane in the following terms.

How little do we have to assume, from a geometric point of view, about an affine plane, in order to be able to describe its points by pairs of elements of a field, and its lines by linear equations?

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 3 , September 1961 , pp. 265 - 278
Copyright
Copyright © Canadian Mathematical Society 1961