\begin{definition}[Definition:Robbins Constant]
The '''Robbins constant''' $R$ is defined as the mean distance $D$ between $2$ points chosen at random from the interior of a unit cube:
{{begin-eqn}}
{{eqn | l = R
      | r = \frac {4 + 17 \sqrt 2 - 6 \sqrt3 - 7 \pi} {105} + \frac {\map \ln {1 + \sqrt 2 } } 5 + \frac {2 \, \map \ln {2 + \sqrt 3} } 5
}}
{{eqn | o = \approx
      | r = 0 \cdotp 66170 \, 71822 \, 67176 \, 23515 \, 582 \ldots
      | c = 
}}
{{end-eqn}}
{{OEIS|A073012}}
\end{definition}