TABLE OF CONTENTS Polygons and polyhedra were among the first forms studied in geometry. Their regularity, symmetry, and orderly lawfulness made them the center of attention of mathematicians, philosophers, artists, architects, and scientists for thousands of years. They are surprisingly simple arrangements of points, lines, and planes. This simplicity, however, harbors subtleties of symmetry and order that deepen our understanding of the physical universe, the atoms of which we are made, and the space-time in which we live.
Polygons are still important today. For example, their use in computer graphics is as common as points and lines, because it is easy to subdivide and approximate the surfaces of solids with planes bounded by polygons. Computer-graphics applications project, fill, and shade these polygonal facets to create realistic images of solids. The study of polygons leads to insights into elementary geometry, algebraic geometry, and number theory.
This chapter discusses two-dimensional polygons whose sides are all straight lines lying in the same plane. Three-dimensional polyhedra whose faces are planar and whose edges are straight lines are the subjects of the next chapter. Polygons and polyhedra also exist in higher-dimension spaces and may have curved edges and faces. Topics covered here include definitions of the various types of polygons, their geometric properties, convex hulls, construction of regular polygons, symmetry, and containment.
A somewhat formal but effective definition goes like this: A polygon is a many sided two-dimensional figure bounded by a closed circuit of straight-line segments joining successive pairs of points. The line...
