Let
be a convex polygon in the plane and suppose that
is positioned in the coordinate system in such a way that
where the
denote the quadrants of the plane. Prove that if
contains no nonzero lattice point, then the area of
is less than
%V0
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 $4.$
Školjka