A note on sets having the Steinhaus property
Abstract
A planar set is said to have the Steinhaus property if however it is placed on
, it contains exactly one integer lattice point. The main result proved in this note is that if a set S satisfying the Steinhaus proper- contains a circle of positive radius, then it contains the disk enclosed by the circle. A result of Mihai Ciucu [2] would then imply that any set having the Steinhaus property cannot contain a circle of positive radius in it.

DOI Code:
10.1285/i15900932v16n1p77
Keywords:
Geometry of numbers; Steinhaus property
Classification:
11H16
Full Text: PDF