Equilateral polygon

Equilateral hexagons

In geometry, an equilateral polygon is a polygon of the Euclidean plane with all sides of the same length. Equilateral polygons are to be distinguished from equiangular polygons in which the interior angles are all the same size. A polygon that is both equilateral and equiangular is called a regular polygon .

definition

A polygon with the sides is called equilateral if the sides of the polygon are all the same length, that is, if ${\displaystyle a,b,c,\ldots }$

${\displaystyle a=b=c=\ldots }$

applies. In an equilateral polygon, all sides are therefore congruent to one another .

Examples

• An equilateral triangle is also an equiangular triangle with interior angles to . ${\displaystyle 60^{\circ }}$
• An equilateral quadrilateral is a diamond with opposing interior angles of equal size.
• A regular polygon is an equilateral polygon that is also equiangular.

properties

• A chord polygon that is equilateral is always equiangular and therefore regular.

• A tangent polygon is equilateral if and only if the interior angles alternate between two values.

• In simple, that is, non- overlapping , equilateral polygons, Viviani's theorem applies , according to which the sum of the distances from any point inside the polygon to the sides of the polygon is independent of the position of the point.

Individual evidence

1. ↑ John M. Lee: Axiomatic Geometry . American Mathematical Society, 2013, pp. 272 .
2. ↑ Michael De Villiers: Equiangular cyclic and equilateral polygons circumscribed . In: Mathematical Gazette . No. 95 , 2011, pp. 102-107 .

Web links

• Eric W. Weisstein : Equilateral Polygon . In: MathWorld (English).
• Wkbj79: Equilateral Polygon . In: PlanetMath . (English)