Date of Award

8-1958

Document Type

Thesis

Degree Name

Master of Science

Department

Master of Mathematics

Abstract

How does one recognize a degenerate conic?

Analytic Geometry textbooks shed unsatisfactory light on this question. Of course, all such books are obliged to make a revelant statement or two in order to dispose of this bothersome subject. But an examination of available reference materials reveals only a single publication* presenting a discussion of somewhat satisfactory dimensions. Elsewhere, observations on degenerate conics are widely scattered and definitely subordinated to more important main topics. Such observations do not support an integrated point-of-view. Students attending courses in Analytic Geometry could be helped immensely by an adequate discussion of degenerate conics.

The purpose of this study is to present a concise elementary discussion of degenerate conics by organizing and interpreting the concepts commonly found in Analytic Geometries. Chapter I outlines the emergence of degenerate conic sections in Synthetic Greek Geometry. Chapter II uses second-degree equations of Coordinate Geometry to identify degenerate conics. The Third Chapter locates degenerate conics through analysis of focus-directrix properties involved in eccentricity. The study closes with a Summary statement and list of References.

*Smith, Salkover, and Justice, Analytic Geometry, 2nd edition, pp. 53-4, 123-8, 271, New York: John Wiley and Sons, Inc., 1954.

Committee Chair/Advisor

A. W. Randall

Publisher

Prairie View A&M College

Rights

© 2021 Prairie View A & M University

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Date of Digitization

10-20-2021

Contributing Institution

John B Coleman Library

City of Publication

Prairie View

MIME Type

Application/PDF

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