4 Feb
2015
4 Feb
'15
8:31 p.m.
(Besides the statistician for the Houston football franchise.) http://en.wikipedia.org/wiki/Simon_Antoine_Jean_L%27Huilier Invented "lim" notation. Also L'Huilier's thm: http://en.wikipedia.org/wiki/Solid_angle#Tetrahedron If the vertex ∠s are a,b,c, the solid angle is 4 ArcTan[Sqrt[Tan[1/4 (a + b - c)] Tan[1/4 (a - b + c)] Tan[1/4 (-a + b + c)] Tan[1/4 (a + b + c)]]] . For a "nice" trig exercise, show this equals one of the alternative expressions I gave here a few years ago: 2 ArcCos[1/4 (1 + Cos[a] + Cos[b] + Cos[c]) Sec[a/2] Sec[b/2] Sec[c/2]] (FullSimplify fails.) --rwg