On the Steinhaus tiling problem in three dimensions
Classical Analysis and ODEs
2013-05-01 v1
Abstract
H. Steinhaus asked in the 1950's whether there exists a set in the plane R^2 meeting every isometric copy of Z^2 in precisely one point. Such a "Steinhaus set" was constructed by Jackson and Mauldin. What about three-space R^3? Is there a subset of R^3 meeting every isometric copy of Z^3 in exactly one point? We offer heuristic evidence that the answer is "no".
Cite
@article{arxiv.1304.8047,
title = {On the Steinhaus tiling problem in three dimensions},
author = {Daniel Goldstein and R. Daniel Mauldin},
journal= {arXiv preprint arXiv:1304.8047},
year = {2013}
}