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The Steinhaus tiling problem and the range of certain quadratic forms

Mihail N. Kolountzakis·Michael Papadimitrakis
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Abstract

We give a short proof of the fact that there are no measurable subsets of Euclidean space (in dimension d > 2), which, no matter how translated and rotated, always contain exactly one integer lattice point. In dimension d=2 (the original Steinhaus problem) the question remains open.

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Mihail N. Kolountzakis, Michael Papadimitrakis. 2000-09-22. The Steinhaus tiling problem and the range of certain quadratic forms. https://arxiv.org/abs/math/0009207

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