Robbins constant

In geometry, the 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{\sqrt {2}}-6{\sqrt {3}}-7\pi }{105}}+{\frac {\ln(1+{\sqrt {2}})}{5}}+{\frac {2\ln(2+{\sqrt {3}})}{5}}.

Its numerical value is approximately [2]

0.66170718226717623515582.

References

Robbins, David P.; Bolis, Theodore S. (1978), "Average distance between two points in a box (solution to elementary problem E2629)", American Mathematical Monthly, 85 (4): 277–278, doi:10.2307/2321177.
Plouffe, Simon, "The Robbins constant", Miscellaneous Mathematical Constants, archived from the original on 2003-05-19

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[1] Robbins, David P.; Bolis, Theodore S. (1978), "Average distance between two points in a box (solution to elementary problem E2629)", American Mathematical Monthly, 85 (4): 277–278, doi:10.2307/2321177.

[2] Plouffe, Simon, "The Robbins constant", Miscellaneous Mathematical Constants, archived from the original on 2003-05-19