Geodesic
On a lattice problem of H. Steinhaus
Jackson, Steve1 ; Mauldin, R.1
1Department of Mathematics, University of North Texas, Denton, Texas 76203
Journal of the American Mathematical Society, Tome 15 (2002) no. 4, pp. 817-856
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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.
DOI : 10.1090/S0894-0347-02-00400-9

Jackson, Steve  1   ; Mauldin, R.  1

1 Department of Mathematics, University of North Texas, Denton, Texas 76203 
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Jackson, Steve; Mauldin, R. On a lattice problem of H. Steinhaus. Journal of the American Mathematical Society, Tome 15 (2002) no. 4, pp. 817-856. doi: 10.1090/S0894-0347-02-00400-9

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