equiangular polygon

A polygonMathworldPlanetmathPlanetmath is equiangular if all of its interior anglesMathworldPlanetmath are congruent.

Common examples of equiangular polygons are rectanglesMathworldPlanetmathPlanetmath and regular polygonsMathworldPlanetmath such as equilateral trianglesMathworldPlanetmath and squares.

Let T be a triangleMathworldPlanetmath in Euclidean geometryMathworldPlanetmath, hyperbolic geometry, or spherical geometry. Then the following are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath:

If T is allowed to be a polygon that has more than three sides, then the above statement is no longer true in any of the indicated geometriesMathworldPlanetmath.

Below are some pictures of equiangular polygons drawn in Euclidean geometry that are not equilateral.

Title equiangular polygon
Canonical name EquiangularPolygon
Date of creation 2013-03-22 17:12:43
Last modified on 2013-03-22 17:12:43
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 10
Author Wkbj79 (1863)
Entry type Definition
Classification msc 51-00
Synonym equiangular
Related topic BasicPolygon