[net.math] So you think you know geometry?

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