lew@ihuxr.UUCP (Lew Mammel, Jr.) (01/18/84)
The problem was to find the spherical volume included by the vertex of a tetrahedron at the center of a sphere. Actually, this is pretty easy. The volume included by a solid angle is just 1/3 the solid angle itself. The solid angle formed by the vertex of a regular tetrahedron is an equilateral spherical triangle with angles equal to the dihedral angle of the tetrahedron. Using the "spherical excess" formula for the area, I get a volume of: acos(1/3) - pi/3 ... Right? Lew Mammel, Jr. ihnp4!ihuxr!lew