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The Three Gap Theorem and the Space of Lattices
Univ Bristol, Bristol, England.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2017 (English)In: The American mathematical monthly, ISSN 0002-9890, E-ISSN 1930-0972, Vol. 124, no 8, p. 741-745Article in journal (Refereed) Published
Abstract [en]

The three gap theorem (or Steinhaus conjecture) asserts that there are at most three distinct gap lengths in the fractional parts of the sequence alpha, 2 alpha,..., N alpha, for any integer N and real number alpha. 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.

Place, publisher, year, edition, pages
MATHEMATICAL ASSOC AMER , 2017. Vol. 124, no 8, p. 741-745
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Mathematical Analysis
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URN: urn:nbn:se:uu:diva-340956DOI: 10.4169/amer.math.monthly.124.8.741ISI: 000413955200008OAI: oai:DiVA.org:uu-340956DiVA, id: diva2:1182202
Funder
EU, FP7, Seventh Framework Programme, 291147Swedish Research Council, 621-2011-3629Available from: 2018-02-12 Created: 2018-02-12 Last updated: 2018-02-12Bibliographically approved

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Strömbergsson, Andreas

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