Bulletin of Symbolic Logic

Research Article

Survey of the Steinhaus Tiling Problem

Steve Jacksona1 * and R. Daniel Mauldina1 

a1 Department of Mathematics, BOX 311430, University of North Texas, Denton, TX 76203, USA E-mail: jackson@unt.edu, E-mail: mauldin@unt.edu


We survey some results and problems arising from a classic problem of Steinhaus: Is there a subset S of ℝ2 such that each isometric copy of ℤ2 (the lattice points in the plane) meets S in exactly one point.

(Received June 22 2003)

(Revised June 25 2003)


*  Research supported by NSF Grant DMS-0097181

  Research supported by NSF Grant DMS-0100078