A Study Of Some Finite Geometries

Author

Ruthie Caldwell, Prairie View Agricultural And Mechanical College

Date of Award

8-1970

Document Type

Thesis

Degree Name

Master of Science

Degree Discipline

Mathematics

Abstract

The geometry studied in high school deals with infinite sets of points and lines. But the geometries which the writer shall consider in this paper contain only a finite number of points and lines. Such geometries are called finite geometries.

It was G. Fano who, in 1892, first considered a finite geometry. Finite geometries were not brought into prominence until 1906 when Oswald Veblen and W, H. Bussey made a study of them. Since that time the study of finite geometries has grown considerably.

In the study of finite geometry, one must remember not to read a meaning into the undefined terms line and point, We must forget the Euclidean properties of a line and think of it as only a collection of points.

The purpose of this paper is to show that the existence of finite geometries furnishes additional support of the hypothetico-deductive nature of much of the present-day geometric study. We shall be concerned with the development of several of the finite goemetries. In each case we shall try to prove as many theorems as possible from a given set of axioms for the geometry. A comparison will also be made of some of the properties of one finite geometry with the properties of another finite geometry. The principle of duality will be studied and a brief comparison of a finite geometry with ordinary Euclidean geometry shall be given.

Committee Chair/Advisor

Fredrick R. Gay

Committee Member

A.D. Stewart

Committee Member

E.E. Thornton

Committee Member

W. Webster

Committee Member

G.H. Stafford

Publisher

Prairie View Agricultural And Mechanical College

Rights

Date of Digitization

3/24/2022

Contributing Institution

John B Coleman Library

City of Publication

Prairie View

MIME Type

Application/PDF

Recommended Citation

Caldwell, R. (1970). A Study Of Some Finite Geometries. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1391