  We consider the distribution of free path lengths, or the distance between
consecutive bounces of random particles, in an n-dimensional rectangular box.
If each particle travels a distance R, then, as R tends to infinity the free
path lengths coincides with the distribution of the length of the intersection
of a random line with the box (for a natural ensemble of random lines) and we
give an explicit formula (piecewise real analytic) for the probability density
function in dimension two and three.
  In dimension two we also consider a closely related model where each particle
is allowed to bounce N times, as N tends to infinity, and give an explicit
(again piecewise real analytic) formula for its probability density function.
  Further, in both models we can recover the side lengths of the box from the
location of the discontinuities of the probability density functions.
