  The Three Gap Theorem states that for any $\alpha \in \mathbb{R}$ and $N \in
\mathbb{N}$, the fractional parts of $\{ 0\alpha, 1\alpha, \dots, (N - 1)\alpha
\}$ partition the unit circle into gaps of at most three distinct lengths. We
prove a result about symmetries in the order with which the sizes of gaps
appear on the circle.
