Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The three gap theorem and the space of lattices   The three gap theorem (or Steinhaus conjecture) asserts that there are at
most three distinct gap lengths in the fractional parts of the sequence
$\alpha,2\alpha,\ldots,N\alpha$, 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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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg