Revisiting the Hexagonal Lattice: On Optimal Lattice Circle Packing

In this note we give a simple proof of the classical fact that the hexagonal lattice gives the highest density circle packing among all lattices in R2. With the benefit of hindsight, we show that the problem can be restricted to the important class of well-rounded lattices, on which the density function takes a particularly simple form. Our proof emphasizes the role of well-rounded lattices for discrete optimization problems