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...

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

atP intersectsS at most once. The solid angle Ω(S) subtended byS atP is the set of

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

surface of the sphere with centerP and radiusa. 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 fromP to any point on S, r =, and the unit normal

vector is directed away fromP.