The three gap theorem and the space of lattices

Jens Marklof, Andreas Strombergsson

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)
326 Downloads (Pure)


The three gap theorem (or Steinhaus conjecture) asserts that there are at most three distinct gap lengths in the fractional parts of the sequence α, 2α, ⋯, Nα, for any integer N and real number α. This statement was proved in the 1950s independently by various authors. Here we present a different approach using the space of two-dimensional Euclidean lattices.
Original languageEnglish
Pages (from-to)741-745
Number of pages5
JournalAmerican Mathematical Monthly
Issue number8
Early online date1 Oct 2017
Publication statusPublished - Oct 2017


Dive into the research topics of 'The three gap theorem and the space of lattices'. Together they form a unique fingerprint.

Cite this