It is known that the directions of all vectors {x, y, z} for which x 2 + y 2 + z 2  n are uniformly distributed in the limit of large n .

Applications of randomness Random drawing of lots has been used throughout recorded history as an unbiased way to distribute risks or rewards.

For if its charge was distributed over a sphere of radius r , this was expected to lead to electrostatic repulsion energy proportional to 1/r .