ThisThe case $h=0$ is known as the *Three"Three-Distance Theorem" -Theorem"; just Googlegoogle for lots ofnumerous references. A randomly selected one: or look here for discussion and nice pictures, or http://www.theoremoftheday.org/NumberTheory/ThreeDistance/TotDThreeDistance.pdfhere for an interesting historical comment.
According to WikipediaA standard reformulation of the theorem is as follows: if, it was conjecturedfor an irrational $\alpha$, the unit-length circle is partitioned "in the natural way" into $n$ arcs by Hugo Steinhausthe points $\alpha k$ with $k\in[1,n]$, then the lengths of these $n$ arcs take just two or three distinct values. This easily implies the case $h\ne 0$ where you basically select one of the arcs (that containing the point corresponding to $h$) and proved by Vera Sosconfine to the lengths of the remaining $n-1$ arcs.