Buffon's Needle Problem

I've come across this in my first probability class. The problem goes that there are a set of parallel lines spaced at "2b" distance apart and there is a needle of length "2a". Assuming a < b.The needle is dropped randomly and the problem is to find the probability that the needle crosses the line. Ans: (2a)/(b*pi)

There is an interesting side to this problem. Apart from probability this problem links up geometry and by this formula we can actually derive the value for pi.
pi = 2a/(b*P)
where P = measured probability. Let us use the relative frequency method to calculate P. Assume N needles are thrown once(which is equivalent to saying one needle is thrown N times.) and say Nr of them cross the lines. Hence P = Nr/N.

It is interesting to know that for a small number like N = 100, the calculated value of pi deviates from the standard value for pi by 1%....

I was really astonished to see something(the experiment) which is probabilistic to actually use to measure something deterministic(pi) :-)