Cube Point Picking

Cube point picking is the three-dimensional case of hypercube point picking.

The mean distance from a point chosen uniformly inside a unit cube to its center is given by

			(1)
			(2)
			(3)
			(4)

Similarly, the mean distance from a point chosen uniformly inside a unit cube to a fixed corner is given by

			(5)
			(6)
			(7)
			(8)
			(9)

where is the -box integral.

The mean distance from the center of a unit cube to a point chosen uniformly on a given face is

			(10)
			(11)
			(12)
			(13)

(OEIS A097047).