I like it! Is there a generalization to n dimensions? Presumably dot products and triple products give way to determinantal expressions. Jim Propp On Saturday, February 20, 2016, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
I came across an interesting formula in an optics book for the solid angle of a spherical triangle. Let a, b, c, be the unit vectors from the center to the vertices of a spherical triangle on the unit sphere. Then the solid angle Omega, which equals the area of the triangle, is given by
tan(Omega/2) = [a,b,c] / (1 + b.c + a.c + a.b),
where a.b etc. are dot products, and [a,b,c] is the scalar triple product. This paper is the cited reference.
http://www.maa.org/sites/default/files/Eriksson14108673.pdf
-- Gene
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