## All Theses

8-1970

Thesis

#### Degree Name

Master of Science

#### Department

Master of Mathematics

#### Abstract

Introduction and Terminology

The fundamental ideas of analytic geometry are usually attributed to the French mathematician and philosopher Descartes (1596-1650). The key to the expression of geometric facts in algebraic form lies in the representation of a point in the plane by means of a pair of real numbers called the coordinates of the point. This paper is devoted to some detailed proofs of fundamental theorems in High School Geometry based on an alternative approach.

The analytic geometry approach seems to be a more powerful attack upon many of the problems of High School Geometry than the methods which we have thus far employed. Analytic geometry not only simplifies the proofs of many of the propositions with which we are familiar, but enables us to attack successfully problems which we could handle in elementary geometry only with great difficulty, or not at all. With the tools already developed- the formulas for distance, point of division (midpoint), and slope- will aid in solving many problems of High School Geometry.

In analytic geometry, the methods of algebra are combined with those of Euclidean geometry in the solution of geometry problems. The properties of a geometric figure depend upon the relations of the parts and not upon the particular position which the figure is drawn. Therefore, the properties of any geometric figure are independent of the way in which the axes are chosen. In the pr~of of geometric properties of figures it will, in general, be possible to choose the axes in more than one way The axes will be chosen in the way which gives the simplest algebra.

The writer would like to point out that analytic geometry is not a different geometry but is a different approach to geometry. This approach was used to prove theorems previously developed by the synthetic approach. In all such cases the analytic proof is not the only proof, but in many cases, it is a far simpler proof.

A. D. Stewart

#### Publisher

Prairie View Agricultural And Mechanical College

#### Rights

© 2021 Prairie View A & M University

4/13/2022

#### Contributing Institution

John B Coleman Library

Prairie View

Application/PDF

COinS