Polygons

Overview

A polygonal chain is a curve specified by a sequence of points $⟨A_1,A_2,\dots ,A_n⟩$ called its vertices. The curve consists of line segments connecting the consecutive vertices. Such a chain is closed if the first vertex coincides with the last.

A simple polygonal chain is a polygonal chain in which only consecutive segments intersect and only at their endpoints. Otherwise it is self-intersecting.

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. It is simple if formed from a simple polygonal chain. Otherwise it is self-intersecting.

Regular

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Figurate Numbers

A polygonal number is any number of pebbles that can be arranged into the shape of a regular filled polygon. A figurate number refers to any polygonal number or their generalizations to other dimensions.