Common
Three-gap theorem
On distances between points on a circle
Three-gap theorem
In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places n {\displaystyle n} points on a circle, at angles of θ , 2 θ , 3 θ , . . . {\displaystyle \theta ,2\theta ,3\theta ,...} from the starting point, then there will be at most three distinct distances between pairs of points in adjacent positions around the circle. When there are three distances, the largest of the three always equals the sum of the other two. Unless θ {\displaystyle \theta } is a rational multiple of π {\displaystyle \pi } , there will also be at least two distinct distances. This result was conjectured by Hugo Steinhaus, and proved in the 1950s by Vera T. Sós, János Surányi, and Stanisław Świerczkowski; more...
Open boosters, collect cards and trade them. Free to play.
Play for free