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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
Volume124
Issue number8
Early online date1 Oct 2017
DOIs
DateAccepted/In press - 14 Dec 2016
DateE-pub ahead of print - 1 Oct 2017
DatePublished (current) - Oct 2017

Abstract

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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  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via MAA at http://www.jstor.org/stable/10.4169/amer.math.monthly.124.8.741. Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 174 KB, PDF document

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