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单词 EquiangularPolygon
释义

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:

  • T is equilateral;

  • T is equiangular;

  • T is regularPlanetmathPlanetmath.

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.

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更新时间:2025/5/4 6:04:17