Van Ravenstein, Tony The three gap theorem (Steinhaus conjecture). (English) Zbl 0663.10039 J. Aust. Math. Soc., Ser. A 45, No. 3, 360-370 (1988). Author’s abstract: “This paper is concerned with the distribution of N points placed consecutively around the circle by an angle of \(\alpha\). We offer a new proof of the Steinhaus Conjecture which states that, for all irrational \(\alpha\) and all N, the points partition the circle into arcs or gaps of at least two, and at most three, different lengths. We then investigate the partitioning of a gap as more points are included on the circle. The analysis leads to an interesting geometrical interpretation of the simple continued fraction expansion of \(\alpha\).” Reviewer: P.Kiss Cited in 3 ReviewsCited in 29 Documents MSC: 11J71 Distribution modulo one 11J04 Homogeneous approximation to one number 11B75 Other combinatorial number theory Keywords:partition of circle; distance of points; Steinhaus Conjecture; simple continued fraction PDF BibTeX XML Cite \textit{T. Van Ravenstein}, J. Aust. Math. Soc., Ser. A 45, No. 3, 360--370 (1988; Zbl 0663.10039) OpenURL Online Encyclopedia of Integer Sequences: Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.