Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square.
random line segments can be picked in a unit square
in the Wolfram Language using the
function RandomPoint[Rectangle[],
n,
2].

Picking two points at random from the interior of a unit square, the average distance between them is the case of hypercube line
picking, i.e.,

The th
raw moment is given for , 4, 6, ... as 1/3, 17/90, 29/210, 187/1575, 239/207, ...
(OEIS A103304 and A103305).

If, instead of picking two points from the interior of a square, two points are chosen at random on different sides of the unit square,
the average distance between two points picked in this manner is

(9)

(10)

(11)

(12)

(OEIS A091506; Borwein and Bailey 2003, p. 25;
Borwein et al. 2004, p. 66).