Journal
AMERICAN MATHEMATICAL MONTHLY
Volume 124, Issue 8, Pages 741-745Publisher
MATHEMATICAL ASSOC AMER
DOI: 10.4169/amer.math.monthly.124.8.741
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Funding
- European Research Council under the European Union's Seventh Framework Programme / ERC [291147]
- Goran Gustafsson Foundation for Research in Natural Sciences and Medicine
- Swedish Research Council [621-2011-3629]
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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.
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