Elements of 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. Analytic planar geometry is the study of planar geometry through the application of coordinate systems. Planar geometry is the study of geometry when only points and geometric figures in a given plane are considered.We are, thus, led to discuss geometry. Geometry is the study of points and sets of points. In this book, a set of points will be referred to as a geometric figure. For example, as we will discuss below, a square can be seen as the union of four segments (its four sides), where each of the four segments, in turn, is sets of points. Thus, a square can be seen as a set of points and, therefore, a square is a “geometric figure.” In this chapter, we will introduce the axioms and axiomatic definitions of geometry used in this book.