MathDB

Let

K

be a convex polygon in the plane and suppose that

K

is positioned in the coordinate system in such a way that

\text{area } (K \cap Q_i) =\frac 14 \text{area } K \ (i = 1, 2, 3, 4, ),

where the

Q_i

denote the quadrants of the plane. Prove that if

K

contains no nonzero lattice point, then the area of

K

is less than

4.

Problem Statement