Minimal Area of a Voronoi Cell in a Packing of Unit Circles
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 $2\sqrt{3}$, and the minimum is achieved only on a perfect hexagon. The proof is short and, in our opinion, instructive.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2022
- DOI:
- 10.48550/arXiv.2211.03255
- arXiv:
- arXiv:2211.03255
- Bibcode:
- 2022arXiv221103255M
- Keywords:
-
- Mathematics - Metric Geometry;
- 51M04;
- 51M05