Open AccessSets meeting isometric copies of the lattice Z 2 in exactly one point
Author(s) -
Steve Jackson,
R. Daniel Mauldin
Publication year - 2002
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.222551699
Subject(s) - isometric exercise , combinatorics , lattice (music) , mathematics , point (geometry) , physics , geometry , medicine , physical therapy , acoustics
The construction of a subset S of (2) such that each isometric copy of (2) (the lattice points in the plane) meets S in exactly one point is indicated. This provides a positive answer to a problem of H. Steinhaus [Sierpiński, W. (1958) Fund. Math. 46, 191-194].