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From: lew@ihuxr.UUCP (Lew Mammel, Jr.)
Newsgroups: net.math
Subject: Re: So you think you know geometry?
Message-ID: <844@ihuxr.UUCP>
Date: Wed, 18-Jan-84 15:00:17 EST
Article-I.D.: ihuxr.844
Posted: Wed Jan 18 15:00:17 1984
Date-Received: Thu, 19-Jan-84 05:32:31 EST
Organization: AT&T Bell Labs, Naperville, IL
Lines: 12

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