The Steinhaus tiling problem and the range of certain quadratic forms
Mihail N. Kolountzakis, Michael Papadimitrakis
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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