Geometriae Dedicata

, Volume 136, Issue 1, pp 175–190 | Cite as

The Three Gap Theorem and Riemannian geometry

  • Ian BiringerEmail author
  • Benjamin Schmidt
Original Paper


The classical Three Gap Theorem asserts that for a natural number n and a real number p, there are at most three distinct distances between consecutive elements in the subset of [0,1) consisting of the reductions modulo 1 of the first n multiples of p. Regarding it as a statement about rotations of the circle, we find results in a similar spirit pertaining to isometries of compact Riemannian manifolds and the distribution of points along their geodesics.


Three Gap Theorem Geodesic flow Riemannian manifold 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.University of ChicagoChicagoUSA

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