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]

${\displaystyle {\frac {4+17{\sqrt {2}}-6{\sqrt {3}}-7\pi }{105}}+{\frac {\ln(1+{\sqrt {2}})}{5}}+{\frac {2\ln(2+{\sqrt {3}})}{5}}.}$

Its numerical value is approximately [2]

${\displaystyle 0.66170718226717623515582.}$