
A polygon ^{1)} is a closed
curve, composed of straight line parts. This page describes simple
polygons. An equilateral polygon has sides of equal length, an equiangular polygon has equal angles. Only for a triangle the equilateral and equiangular version gives the same figure. The two qualities together make a regular polygon. The more sides the polygon has, the more it approximates a circle. The genius mathematician Gauss showed  in the age of 18  which regular polygons can be constructed with a pair of compasses and a ruler ^{2)}. For example the regular heptadecagon has this quality. The polygons have been given own names, derived from the Greek numerals: The first two polygons mentioned are onedimensional, they consist both of just one side. Some polygons derive their qualities in relation to their position according another curve:
A socalled control polygon is used to define a curve by points near the curve, not by points on the curve. In the field of Roman ancient history the so called Thijssen polygons are in use: these polygons have been constructed around Roman district capitals, to approximate the districts' boundaries. I dedicated a separate page to the family of stars. notes 1) Poly (Gr.) = many, goonia (Gr.) = angle. 2) When n is the number of sides, then for be able to construct by a pair of compasses, n has to obey: 