[math-fun] Spherical trig question

David Wilson>On the unit sphere, measuring angles in radians. Place an arc with measure A on the equator. Place arcs with measures B and C at each end of A running north along meridians (perpendicular to A). Join the northern endpoints of B and C with a great circle arc. What is the area of the spherical quadrilateral thus formed? rwg>If you know the angles between those arc at those endpoints to be a, isn't it just the angular excess 2 a + 2 pi - 2 pi = 2a? If you know all four arcs, max_solid_angle(a,b,c,d):=2*acos((cos(d)+cos(c)+cos(b)+cos(a))/(4*cos(a/2)*cos(b/2)*cos(c/2)*cos(d/2))-tan(a/2)*tan(b/2)*tan(c/2)*tan(d/2)) --rwg