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Filtering by: Advisor Goheen, Harry Language English [eng] Subject Geometry, Non-Euclidean

Finite non-projective geometries without the axiom of parallels

Creator:

Henderson, Mason Edward

Resource Type:

Masters Thesis
A model of Non-Euclidean geometry in three dimensions

Creator:

Zell, William Lee

Abstract:

In this paper we present a model of Non-Euclidean geometry in three dimensions. This will show that the axioms of Non-Euclidean geometry are consistent if Euclidean geometry and, hence, arithmetic is consistent. However, the model is incomplete for we have not included the topic of congruence, the axiom of Archimedes,...

Resource Type:

Masters Thesis
Finite geometries without the axiom of parallels

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...

Resource Type:

Dissertation
The completeness axiom of Lobachevskian geometry

Creator:

Hartvigson, Zenas Russell

Abstract:

This paper gives a proof that the Completeness Axiom of Lobachevskian geometry -- as formulated in the second English translation of David Hilbert's Foundations of Geometry (tenth German edition)--is a theorem in the three dimensional Poincare model. An explicit canonical isomorphism between all models of Lobachevskian space is given. This,...

Resource Type:

Dissertation