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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

On a lattice problem of H. Steinhaus


Authors: Steve Jackson and R. Daniel Mauldin
Journal: J. Amer. Math. Soc. 15 (2002), 817-856
MSC (2000): Primary 04A20; Secondary 11H31
Published electronically: June 13, 2002
MathSciNet review: 1915820
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that there is a subset $S$ of $\mathbb{R} ^2$such that each isometric copy of $\mathbb{Z} ^2$ (the lattice points in the plane) meets $S$in exactly one point. This provides a positive answer to a problem of H. Steinhaus.


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Additional Information

Steve Jackson
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: jackson@unt.edu

R. Daniel Mauldin
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203
Email: mauldin@unt.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-02-00400-9
PII: S 0894-0347(02)00400-9
Keywords: Lattice points, Steinhaus problem, four-bar linkage
Received by editor(s): February 14, 2001
Received by editor(s) in revised form: October 29, 2001
Published electronically: June 13, 2002
Additional Notes: The first author’s research was supported by NSF Grant DMS-0097181.
The second author’s research was supported by NSF Grant DMS-9801583
Article copyright: © Copyright 2002 American Mathematical Society