(simple) polygon
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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:
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:
where pi is the
Fermat Number for which:
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