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 ( of each angle of a biangle. Then the biangle covers ( 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.

Title biangle
Canonical name Biangle
Date of creation 2013-03-22 17:06:10
Last modified on 2013-03-22 17:06:10
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 8
Author Wkbj79 (1863)
Entry type Definition
Classification msc 51M10
Classification msc 51-00