Girard's Theorem states that the sum of the angles of a triangle drawn on a sphere is not 180 degrees but the sum differs from 180 degrees by the area of the triangle divided by the radius squared.
I have a generalised function in spherical polar co-ordinates that describes the radiant intensity in any given direction of a point source emitter. I need to calculate the fraction of the total radiation that is emitted into a region of space specified by some min to max range of elevation...