The Steinhaus tiling problem and the range of certain quadratic forms
Classical Analysis and ODEs
2007-05-23 v1 Metric Geometry
Number Theory
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.
Cite
@article{arxiv.math/0009207,
title = {The Steinhaus tiling problem and the range of certain quadratic forms},
author = {Mihail N. Kolountzakis and Michael Papadimitrakis},
journal= {arXiv preprint arXiv:math/0009207},
year = {2007}
}