Date of Award
Master of Science
Master of Mathematics
This paper is an attempt to give a development of the parabola and some of its properties by the methods of synthetic geometry. The writer also wishes to show the power and beauty of synthetic geometry in proving theorems pertaining to the parabola.
The basic problem is to formulate and prove at least fifteen theorems using only synthetic geometry. The usual approach to properties of conics such as the parabola is by means of analytic geometry. Yet, in a traditional course in high school geometry, most of the theorems on lines and line segments, angles, triangles, quadrilaterals, and circles are proved using only a synthetic approach.
The writer was motivated to do research in this area for primarily two reasons. First, there was the desire to know if the synthetic method can indeed be used to study properties of a parabola since it is such a powerful method in the study of triangles, quadrilaterals, and circles. Secondly, the writer wanted to discover, study and prove some of the lesser-known — that is, to the writer — properties of the parabola and to see how effectively the synthetic approach can be used in this study.
Frederick R. Gray
Prairie View Agricultural and Mechanical College
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Date of Digitization
John B Coleman Library
City of Publication
Dooley, B. L. (1970). A Development Of The Parabola And Some Of Its Properties By The Synthetic Methods Of High School Geometry. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1432