Parallelogram Law (Inner Product Space)

Theorem
Let $H$ be a Hilbert space with associated norm $\norm {\, \cdot \,}$.

Let $f,g \in H$ be arbitrary.

Then:
 * $\norm {f + g}^2 + \norm {f - g}^2 = 2 \paren {\norm f^2 + \norm g^2}$