Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: MITSUNORI IMAOKA and TATSUYA YAMASHITA
Pages: [389] - [400]
Received Date: August 5, 2008
Submitted by:
Schoenberg has given a characterization of the set of points at different distances from all rational lattice points. It was motivated from a solution of Sierpiński on a problem of Steinhaus, and the problem was originally asked to the integral lattice points. In this article, we study how far Schoenberg’s method can be applied to the points at different distances from all integral lattice points, and show a complete description in case of the plane.
lattice points, Steinhaus problem, irrational numbers.
