TABLE OF CONTENTS Technical shop mathematics relies on plane geometry, the study of the properties and relationships of figures including points, lines, and polygons, which lie in the two-dimensional plane, and polyhedrons, which exist in three-dimensional space.
The word geometry is from the Greek words meaning the measure of the earth.
Points as locations are studied in analytic geometry, which provides ways to graph plane figures in the Cartesian plane and describe them with algebraic methods.
We begin with points, the most fundamental of geometric figures. A point is zero-dimensional it has no length, width, or thickness. However, to draw a picture of a point, we usually draw a dot, which necessarily has dimension a pencil mark, for example, or a pixel on a computer screen. Figure 15.1 shows a typical illustration of a point.
A single point can denote a location in space. When connected, points form one-, two-, and three-dimensional geometric figures.
We intuitively understand what fundamental geometric figures look like. Defining them is not so easy. Let us agree that a line is a set of points existing in one dimension: length. A line s length is infinite. Lines may be either straight or curved. A curved line continually changes direction. A straight line does not change direction. In this discussion, we always mean a straight line when we use the word line.
Although an illustration of a line has finite...
