an:04083739
Zbl 0663.10039
Van Ravenstein, Tony
The three gap theorem (Steinhaus conjecture)
EN
J. Aust. Math. Soc., Ser. A 45, No. 3, 360-370 (1988).
00169337
1988
j
11J71 11J04 11B75
partition of circle; distance of points; Steinhaus Conjecture; simple continued fraction
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 \(\alpha\).''
P.Kiss