New characterizations of inner product spaces among normed spaces involving the notion of strong convexity are given. In particular, it is shown that the following conditions are equivalent: (1) (X,k · k) is an inner product space; (2) f : X ! R is strongly convex with modulus c > 0 if and only if f ck · k 2 is convex; (3) k · k 2 is strongly convex with modulus 1.