(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
Why do microwave ovens alternate between rotating the
food-carousel clockwise and rotating it counterclockwise (or, as the Brits
would say, anticlockwise)?
Jim Propp
