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
DOI:
https://doi.org/10.1090/S0894-0347-02-00400-9
Published electronically:
June 13, 2002
MathSciNet review:
1915820
Full-text PDF Free Access
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
MR Author ID:
255886
ORCID:
0000-0002-2399-0129
Email:
jackson@unt.edu
R. Daniel Mauldin
Affiliation:
Department of Mathematics, University of North Texas, Denton, Texas 76203
Email:
mauldin@unt.edu
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
