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arXiv · 0911.4106

Revisiting the hexagonal lattice: on optimal lattice circle packing

Lenny Fukshansky
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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 $R^2$. 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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Lenny Fukshansky. 2009-11-20. Revisiting the hexagonal lattice: on optimal lattice circle packing. https://arxiv.org/abs/0911.4106

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