Robbins constant

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In geometry, Robbins' constant, named after David P. Robbins, is the average distance between two points selected at random within a unit cube. Robbins' constant can be expressed as [1]

\frac{4+17\sqrt2-6\sqrt3-7\pi}{105} + \frac{\ln(1+\sqrt2)}{5} + \frac{2\ln(2+\sqrt3)}{5}.

Its numerical value is approximately [2]

0.66170718226717623515583.

[edit] References

  1. ^ D. Robbins, Average distance between two points in a box, American Mathematical Monthly, 85 (1978) p. 278
  2. ^ Miscellaneous Mathematical Constants by Simon Plouffe
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