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单词 Biangle
释义

biangle


In spherical geometryMathworldPlanetmath, it is possible to form a polygonMathworldPlanetmathPlanetmath with only two sides. Thus, we have the following definition:

A biangle is a two-sided polygon that is strictly contained in one hemisphere of the sphere that is serving as the model for spherical geometry.

Given a biangle, its vertices must be antipodal points, and its two angles must be congruent. Therefore, every biangle is equiangular. Since each side of a biangle is half of a great circle, every biangle is equilateral. Hence, every biangle is regularPlanetmathPlanetmathPlanetmath.

Let θ be the radian measure (http://planetmath.org/AngleMeasure) of each angle of a biangle. Then the biangle covers (http://planetmath.org/Cover) θ2π of the sphere. Since the area of the sphere is 4π, the area of the biangle is 2θ. Note that this equals the angle sum of the biangle.

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更新时间:2025/5/4 8:29:18