Buffon's needle experiment

If you drop N needles of length L onto a floor with strips of width 2L, the ratio of N and the number of needles across lines is approximately π. In other words, the probability of a needle crossing a line is 1/π.

[@ThePigasaurus]

Super cool demonstration! Thanks for making this it was just what I was looking for

[@fightingforcatalonia]

Does it really converge with N tending to infinity?

[@skylardeslypere9909]

It does. If you want I can provide a full explanation but here's a short one:
If you drop one needle with length L < d on a sheet of infinitely many lines a distance of d apart, the probablity that this needle will cross a line is exactly 2L/(pi*d)
So if d = 2L, then the probability of a needle crossing a line is 1/pi
That means for any N, the expected ratio of needles that cross the line is 1/pi, which obviously becomes more accurate as N tends to infinity

[@thenerdguy9985]

Ever heard of law of large numbers?

[@Theonegamefreak]

@@skylardeslypere9909 how do you derive that probability?

[@ivanlai5467]

@@Theonegamefreak there's a lot of resources and how to derive it online. Just google it.