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The three gap theorem and the space of lattices

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)741-745
Number of pages5
JournalAmerican Mathematical Monthly
Issue number8
Early online date1 Oct 2017
DateAccepted/In press - 14 Dec 2016
DateE-pub ahead of print - 1 Oct 2017
DatePublished (current) - Oct 2017


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.

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