The three gap theorem (or Steinhaus conjecture) asserts that there are at most three distinct gap lengths in the fractional parts of the sequence α, 2α, ⋯, Nα, for any integer N and real number α. 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.
|Number of pages||5|
|Journal||American Mathematical Monthly|
|Early online date||1 Oct 2017|
|Publication status||Published - Oct 2017|