MathDB

4

Part of 1998 Romania Team Selection Test

Problems(1)

Unit square grid not intersecting any segments in finite set

Source: Romania TST 1998

4/23/2011
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
analytic geometrytrigonometryfunctioncombinatorics proposedcombinatorics