Aneesh Dasgupta

Symmetries of the Three Gap Theorem

The Three Gap Theorem states that for any $α\in \mathbb{R}$ and $N \in \mathbb{N}$, the fractional parts of $\{ 0α, 1α, \dots, (N - 1)α\}$ 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.