Summary: 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) \((X,\|\cdot\|)\) is an inner product space; (2) \(f : X\to\mathbb R\) is strongly convex with modulus \(c>0\) if and only if \(f-c\|\cdot\|^2\) is convex; (3) \(\|\cdot\|^2\) is strongly convex with modulus 1.