Educação Superior::Ciências Exatas e da Terra::MatemáticaLet α be a real number, and consider the arithmetic progression 0, α, 2α, 3α, ..., nα modulo 1. You can think of this as walking along a circle with n steps of a fixed length. The three-distance theorem states that the distance between any two consecutive footprints is one of at most three distinct numbers. That is, the circle is partitioned into arcs with at most three distinct lengths