### 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.