MathDB
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 2\sqrt{2}. 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