Weyl's_tube_formula
Weyl's tube formula gives the volume of an object defined as the set of all points within a small distance of a manifold.
Let be an oriented, closed, two-dimensional surface, and let denote the set of all points within a distance of the surface . Then, for sufficiently small, the volume of is
where is the area of the surface and is its Euler characteristic. This expression can be generalized to the case where is a -dimensional submanifold of -dimensional Euclidean space .