where k ? k(s) > 0 is the curvature function of C and ds signifies arclength measure on C. Equality holds if and only if C is a circle. In [1], two proofs of this result are given: the first uses a polygonal approximation of the curve C; the second is based on ideas of Osserman [4]. In this note we give a very short new proof of (1), which has the advantage of providing a geometric interpretation of the difference 2F ? fck~[ds. To be precise, we prove that
