Buffon's Needle Experiment

Buffon's Floor
Scatter plot
Distribution graph Pi Estimate graph

Description

Buffon's needle experiment is a random experiment that results in a statistical estimation of the number \(\pi\). The experiment consists of dropping a needle on hardwood floor, with floorboards of width 1. The experiment is shown graphically in the picture box. Random variable \(X\) gives the angle of the needle relative to the floorboard cracks and random variable \(Y\) gives the distance from the center of the needle to the lower crack. These variables are recorded in the data table on each update. Each point \((X, Y)\) is shown as a red dot in the scatterplot. Random variable \(I\) indicates the event that the needle crosses a crack. The probability density function of \(I\) is shown in blue in the distribution graph and is recorded in the distribution table. On each update, the empirical density function of \(I\) is shown in red in the distribution graph and is also recorded in the distribution table. Finally, on each update, Buffon's estimate of \(\pi\) is shown in red in the estimate graph and is recorded in the estimate table. The parameter is the needle length \(L\), which can be varied with a scrollbar.