  The three gap theorem (or Steinhaus conjecture) asserts that there are at
most three distinct gap lengths in the fractional parts of the sequence
$\alpha,2\alpha,\ldots,N\alpha$, for any integer $N$ and real number $\alpha$.
This statement was proved in the 1950s independently by various authors. Here
we present a different approach using the space of two-dimensional Euclidean
lattices.
