English

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.

Keywords

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}
}
R2 v1 2026-07-22T16:34:51.847Z