The Steinhaus tiling problem and the range of certain quadratic forms

2000/09/22 by Mihail N. Kolountzakis, Kolountzakis, Mihail N., Michael Papadimitrakis +1 · 1 citation
Mathematics · #11E25 #52C22 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT) #math.CA #math.MG #math.NT #msc:11E25 #msc:52C22

paper · pdf · doi:10.48550/arxiv.math/0009207

arxiv created 2000/09/22 · arxiv updated 2009/11/30

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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