Revisiting the hexagonal lattice: on optimal lattice circle packing

Details Revisiting the hexagonal lattice: on optimal lattice circle packing Revisiting the hexagonal lattice: on optimal lattice circle packing

2009-11-20

arxiv.org/abs/0911.4106v1

Elemente der Mathematik, vol. 66 no. 1 (2011) pg. 1--9

Mathematics

Number Theory

8 pages, 1 figure; to appear in Elemente der Mathematik

Scientific paper

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 $R^2$. 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.

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