Simulation of Buffons Needle

Yihui Xie & Lijia Yu 2017-04-04

This function provides a simulation for the problem of Buffon’s Needle, which is one of the oldest problems in the field of geometrical probability.

This is quite an old problem in probability. For mathematical background, please refer to http://en.wikipedia.org/wiki/Buffon's_needle or http://www.mste.uiuc.edu/reese/buffon/buffon.html.

‘Needles’ are denoted by segments on the 2D plane, and dropped randomly to check whether they cross the parallel lines. Through many times of ‘dropping’ needles, the approximate value of \(\pi\) can be calculated out.

There are three graphs made in each step: the top-left one is a simulation of the scenario, the top-right one is to help us understand the connection between dropping needles and the mathematical method to estimate \(\pi\), and the bottom one is the result for each drop.

## it takes several seconds if 'redraw = TRUE'
ani.options(nmax = 400, 1)
par(mar = c(3, 2.5, 0.5, 0.2), pch = 20, mgp = c(1.5, 0.5, 0))

plot of chunk demo-a

## this will be faster
ani.options(nmax = 400, 1)
buffon.needle(redraw = FALSE)

plot of chunk demo-b