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 regular.
Let be the radian measure (http://planetmath.org/AngleMeasure) of each angle of a biangle. Then the biangle covers (http://planetmath.org/Cover) of the sphere. Since the area of the sphere is , the area of the biangle is . Note that this equals the angle sum of the biangle.
|Date of creation||2013-03-22 17:06:10|
|Last modified on||2013-03-22 17:06:10|
|Last modified by||Wkbj79 (1863)|