Calculating pi by dropping needles

Buffon’s Needle was first stated in 1777 and involves dropping a needle onto lined paper and calculating the probability of the needle crossing one of the lines on the page. Remarkably, this probability is directly related to the value of pi. To calculate pi from the needle drops, one must take the number of drops, multiply this by two, then divide by the number of times it crosses the line. This only works so simply when the distance between the lines is equal to the length of the needle.

If the distance from the centre of the needle to the nearest line is D and the angle at which the needle falls is θ (measured from a line parallel to the lines on the page) then the needle will cross the line if D ≤ (1/2)sin(θ). Find out more and try for yourself here.

Needle in a haystack