Imagine a stick of length 1, and also a floor with evenly spaced lines, such that the distance between neighboring lines is also 1. If one throws the stick on the floor, there will be certain probability that stick crosses a line on the floor. Finding that probability is known as Buffon needle problem.
It turns out that the probability involves $\pi$, and that was really a surprise, and an enigma, for a long time, since there is no circle, or anything circular or curved, involved in problem statement.
Is there a 3D equivalent of Buffon needle?
Does the probability in such case involve $\pi$?
What about N-dimensional equivalent of Buffon needle?