Publication Date

1968

Document Type

Dissertation/Thesis

First Advisor

Saxena, Subhash Chandra, 1934-

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematics

LCSH

Geometry; Plane

Abstract

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.

Comments

Includes bibliographical references.

Extent

50 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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