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{\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]

0.66170718226717623515583.

References

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

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[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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