Buffon's Needle

Theorem
Let a horizontal plane be divided into strips by a series of parallel lines a fixed distance apart, like floorboards.

Let a needle whose length equals the distance between the parallel lines be dropped onto the plane randomly from a random height.

Then the probability that the needle falls across one of the parallel lines is $\dfrac 2 \pi$.

Also known as
This problem is also known just as the needle problem.