Unit square grid not intersecting any segments in finite set
Source: Romania TST 1998
April 23, 2011
analytic geometrytrigonometryfunctioncombinatorics proposedcombinatorics
Problem Statement
Consider in the plane a finite set of segments such that the sum of their lengths is less than . Prove that there exists an infinite unit square grid covering the plane such that the lines defining the grid do not intersect any of the segments.Vasile Pop