Definition:Polygon/Regular

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Definition

A regular polygon is a polygon which is both equilateral and equiangular.

That is, in which all the sides are the same length, and all the vertices have the same angle:

RegularPolygon.png


Center

The center of a regular polygon $P$ is defined as the point which is the center of the circumcircle of $P$.

Regular-Polygon-Center.png

In the above, $O$ is the center of the regular polygon.


Long Radius

The long radius of a regular polygon $P$ is defined as the distance from the center of $P$ to one of its vertices.

Long-radius-of-Polygon.png

In the above, the length of $OA$ is the long radius of the regular polygon.


Apothem

The apothem of a regular polygon $P$ is defined as the perpendicular distance from the center of $P$ to one of its sides.

Apothem.png

In the above, the length of $OM$ is the apothem of the regular polygon.


Also known as

In Euclid's The Elements, a regular polygon is referred to as an equilateral and equiangular polygon.

Some sources use the word perfect or symmetrical instead of regular.


Examples

Specific instances of regular polygons with specific numbers of sides are as follows:


The term regular $n$-gon is usually used nowadays to specify a regular polygon with a specific number, that is $n$, sides.

The specific name is usually invoked only in order to draw attention to the fact that such a regular polygon has a particularly interesting set of properties.


Also see

  • Results about regular polygons can be found here.


Sources

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