Improved bounds for the disk-packing constant

  title={Improved bounds for the disk-packing constant},
  author={D. W. Boyd},
  journal={aequationes mathematicae},
  • D. W. Boyd
  • Published 1973
  • Mathematics
  • aequationes mathematicae
This result lends considerable weight to the heuristic estimate S ~ 1.306951, obtained by Melzak [6]. The improvement is a result of some new inequalities involving the disk-packing function M(a, b, c; t). Our principal new result is that M is a strictly convex function of (a, b, c). This, combined with the fact that M is a symmetric function of these three variables and an auxiliary lemma, allows us to show that 
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