On the lattice diameter of a convex polygon Original Research Article

The lattice diameter, ℓ(P), of a convex polygon P in R2 measures the longest string of integer points on a line contained in P. We relate the lattice diameter to the area and to the lattice width of P, wl(P). We show, e.g., that wl⩽43ℓ+1, thus giving a discrete analogue of Blaschkeʹs theorem.