Revisiting the Hexagonal Lattice: On Optimal Lattice Circle Packing

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow

Document Type

Article

Department

Mathematics (CMC)

Publication Date

2011

Abstract

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.

Rights Information

© 2011 European Mathematical Society (EMS) Publishing House

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

DOI: 10.4171/EM/163

Recommended Citation

Fukshansky, Lenny. "Revisiting the Hexagonal Lattice: on Optimal Lattice Circle Packing." Elemente der Mathematik 66.1 (2011): 1-9. Web.