Well in the sphere and circle cases, it works because if you are expanding size, it expands at the perimeter. In the line case, if your line is 2r, the derivati

Well in the sphere and circle cases, it works because if you are expanding size, it expands at the perimeter. In the line case, if your line is 2r, the derivative is 2. So expanding infinitesimally expands the line by 2 times that amount. So I guess it holds, but maybe isn't all that interesting.