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Density Problems for Packings and Coverings

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Research Problems in Discrete Geometry

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Abstract

In his lecture at the Scandinavian Natural Science Congress in 1892, Axel Thue [Th892] claimed that the density of any arrangement of non-overlapping equal circles in the plane is at most \( \pi /\sqrt {12} \), the ratio of the area of the circle to the area of the regular hexagon circumscribed about it.

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(2005). Density Problems for Packings and Coverings. In: Research Problems in Discrete Geometry. Springer, New York, NY. https://doi.org/10.1007/0-387-29929-7_2

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