MathDB

In the coordinate system in the plane we consider a convex polygon

W

and lines given by equations

x = k, y = m

, where

k

and

m

are integers. The lines determine a tiling of the plane with unit squares. We say that the boundary of

W

intersects a square if the boundary contains an interior point of the square. Prove that the boundary of

W

intersects at most 4 \lceil d \rceil unit squares, where

d

is the maximal distance of points belonging to

W

(i.e., the diameter of

W

) and \lceil d \rceil is the least integer not less than

d.

Problem Statement