Elements of Analytic Planar Geometry

Abstract

Trigonometric functions are fundamental in physics and found throughout physics. Trigonometric functions, in turn, may be defined through the “Trigonometric Circle” in analytic planar geometry. We are thus led to discuss analytic planar geometry. Analytic Planar Geometry is the study of planar geometry through coordinate systems. In a plane, a coordinate system is a relation between points P in the plane and ordered pairs of real numbers (R1,R2) such that each ordered pair of real numbers represents a single point, and each point is represented by at least one ordered pair of real numbers. Through Analytic Planar Geometry, Planar Geometry problems can be analyzed through the properties of real numbers and real number equations (rather than directly through the properties of geometric points). Also, through Analytic Planar Geometry, real number equations can, in turn, be analyzed through the properties of geometric points in Planar Geometry.