Saxena, Subhash Chandra, 1934-
M.S. (Master of Science)
Department of Mathematics
This paper is primarily concerned with exhibiting examples of Non-Desarguesian planes. The first example is of a finite Non-Desarguesian plane, including a method for constructing an analytic projective plane. Since the coordinate set of this finite Non-Desarguesian plane does not have the right distributive property the coordinate set is not a ring. The other three examples cited are real Non-Desarguesian planes. The examples by Hilbert and Sitaram are discussed as projective planes while the example by Moulton is considered as an affine plane. In the three real examples of the Non-Desarguesian planes we find if Desargues' theorem is not valid in a plane then there are also other properties that are not valid in the plane. In Hilbert's plane Pascal's theorem fails. In Sitaram's plane the theorem of Pappus is not valid and in Moulton's plane a ternary ring is not linear.
Johnson, Glen A., "Four examples of Non-Desarguesian planes" (1968). Graduate Research Theses & Dissertations. 3181.
Northern Illinois University
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