Robbins constant

Robbins constant

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 [D. Robbins, "Average distance between two points in a box", American Mathematical Monthly, 85 (1978) p. 278]

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

Its numerical value is approximately [ [http://www.worldwideschool.org/library/books/sci/math/miscellaneousmathematicalconstants/chap80.html Miscellaneous Mathematical Constants by Simon Plouffe] ]

:0.66170718226717623515583.

References


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