Revisiting the hexagonal lattice: on optimal lattice circle packing

In this note we give a simple proof of the classical fact that the hexagonallattice gives the highest density circle packing among all lattices in $R^2$.With the benefit of hindsight, we show that the problem can be restricted tothe important class of well-rounded lattices, on which the density functiontakes a particularly simple form. Our proof emphasizes the role of well-roundedlattices for discrete optimization problems.