Cube point picking is the three-dimensional case of hypercube point picking. The average distance from a point picked at random inside a unit cube to the center is given by d^__center | = | integral_(-1/2)^(1/2) integral_(-1/2)^(1/2) integral_(-1/2)^(1/2) sqrt(x^2 + y^2 + z^2)d x d y d z | = | 8 integral_0^(1/2) integral_0^(1/2) integral_0^(1/2) sqrt(x^2 + y^2 + z^2)d x d y d z | = | 1/8 sqrt(3) - 1/48 π - 1/4 ln2 + 1/2 ln(1 + sqrt(3)) | = | 0.480296....
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