The disk-packing constant

  title={The disk-packing constant},
  author={David W. Boyd},
  journal={aequationes mathematicae},
The lower bound was subsequently improved by Wilker [8] to 1.059, and by the author [2] to 1.28467. An improved upper bound of 1.5403 . . . . (9+x/41)/10 was proved in [3], but the arguments there, although they apply to sphere packings in higher dimensions, are too general in nature to yield a significant improvement of this bound. In this paper, we present a method of attack which gives both upper and lower bounds. In fact, for any integer x, we obtain bounds 2 (K)<S</~(x) such that /z ( x… CONTINUE READING