Let be a smooth parametric surface and let P be a point such that each line that starts

at P intersects S at most once. The solid angle Ω(S) subtended by S at P is the set of

lines starting at P and passing through . Let S(a) be the intersection of Ω(S) with the

surface of the sphere with center P and radius a. Then the measure of the solid angle (in

steradians) is defined to be

Apply the Divergence Theorem to the part of Ω(S) between S(a) and to show that

where is the radius vector from P to any point on S, r = , and the unit normal

vector is directed away from P.

 

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