Finite geometries without the axiom of parallels

Graduate Thesis Or Dissertation

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Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/kh04ds19q

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Attribute Name	Values
Creator	Henderson, Mason Edward
Abstract	Among the geometries with n points on every line (with n an integer greater than one), those in which there are no parallels and those in which the axiom of parallels holds have been discussed (as finite projective and affine geometries) in the literature. This paper contrasts such geometries with a Bolyai-Lobatchevski finite geometry in which there are at least two parallels to a given line at a point not on that line. Existence theorems for the plane are given, as well as methods of construction and identification of certain Steiner systems as planes. The non-existence of k-spaces is proved when k > 3.
Resource Type	Dissertation
Date Available	2010-07-29T16:55:27+00:00
Date Issued	1964-04-30
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	1964
Advisor	Goheen, Harry
Academic Affiliation	Mathematics
Non-Academic Affiliation	Oregon State University. Graduate School
Subject	Geometry, Non-Euclidean
Rights Statement	Copyright Not Evaluated
Publisher	Oregon State University
Language	English [eng]
Digitization Specifications	File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
Replaces	http://hdl.handle.net/1957/17208

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