Jung's Theorem

Theorem
Let $S \subseteq \R^n$ be a compact subspace of an $n$-dimensional Euclidean space.

Let $d = \displaystyle \max_{x, y \mathop \in S} \map d {x, y}$ be the diameter of $S$.

Then there exists a closed ball ${B_r}^-$ with radius $r$ such that:
 * $r = d \sqrt {\dfrac n {2 \paren {n + 1} } }$

such that $S \subseteq {B_r}^-$.