Minimal Area of a Voronoi Cell in a Packing of Unit Circles

2022/11/07 by Mazel, A., Stuhl, I., Suhov, Y.
#51M04 #51M05 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2211.03255

Abstract

We present a new self-contained proof of the well-known fact that the minimal area of a Voronoi cell in a unit circle packing is equal to 2√(3), and the minimum is achieved only on a perfect hexagon. The proof is short and, in our opinion, instructive.

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