Curved Hexagonal Packings of Equal Disks in a Circle

@article{Lubachevsky1997CurvedHP,
  title={Curved Hexagonal Packings of Equal Disks in a Circle},
  author={Boris D. Lubachevsky and Ronald L. Graham},
  journal={Discrete & Computational Geometry},
  year={1997},
  volume={18},
  pages={179-194}
}
For each k ≥ 1 and corresponding hexagonal number h(k) = 3k(k + 1) + 1, we introduce m(k) = max{ (k−1)! 2 , 1} packings of h(k) equal disks inside a circle which we call the curved hexagonal packings. The curved hexagonal packing of 7 disks (k = 1, m(1) = 1) is well known and the one of 19 disks (k = 2, m(2) = 1) has been previously conjectured to be optimal. New curved hexagonal packings of 37, 61, and 91 disks (k = 3, 4, and 5, m(3) = 1, m(4) = 3, and m(5) = 12) were the densest we obtained… CONTINUE READING
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