(simple) polygon

line

last updated: 2006-04-06

A polygon 1) is a closed curve, composed of straight line parts.

In the Netherlands, in the sixties the 'Polygoon' news-reel showed us news from all over the world in the cinema.

This page describes simple polygons.
Another page is dedicated to the (nonsimple) star 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:

number of sides name of polygon
1 henagon or monogon
2 digon
3 triangle
4 quadrilateral
5 pentagon
6 hexagon
7 heptagon
8 octagon
9 enneagon
10 decagon
11 hendecagon
12 dodecagon
13 tridecagon or triskaidecagon
14 tetradecagon
15 pentadecagon, pentakaidecagon or quindecagon
16 hexadecagon or hexakaidecagon
17 heptadecagon, heptakaidecagon, or septadecagon
18 octadecagon or octakaidecagon
19 enneadecagon, enneakaidecagon, or nonadecagon
20 icosagon
21 icosikaihenagon or henicosagon
22 icosikaidigon or docosagon
23 icosikaitrigon or tricosagon
24 icosikaitetragon or tetracosagon
25 icosikaipentagon or pentacosagon
26 icosikaihexagon or hexacosagon
27 icosikaiheptagon or heptacosagon
28 icosikaioctagon or octacosagon
29 icosikaienneagon, enneacosagon or nonacosagon
30 triacontagon
31 triacontakaihenagon or henitriacontagon
32 triacontakaidigon or dotriacontagon
40 tetracontagon
50 pentacontagon
60 hexacontagon
70 heptacontagon
80 octacontagon
90 enneacontagon or nonacontagon
100 hectagon
1000 chiliagon
10000 myriagon
1000000 hecatommyriagon or hekatommyriagon

The first two polygons mentioned are one-dimensional, they consist both of just one side.

Some polygons derive their qualities in relation to their position according another curve:

  • a cyclic polygon is a polygon where the sides are chords of a given circle
  • for a tangent polygon the sides are tangent to a given curve (in most cases a circle)
  • the circumscribed polygon and the inscribed polygon: when on each side of a polygon there lies a vertex of a second polygon, we call the outer polygon a circumscribed polygon, and the inner polygon an inscribed polygon

A so-called 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.

You can also imagine polygons build of circle arcs, these are curvilinear polygons.


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:

h01polyntf.gif (982 bytes)  
where pi is the Fermat Number for which:    h01polyntg.gif (954 bytes)