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
and the bottom one is the result for each drop.
library(animation) ## 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)) buffon.needle()
## this will be faster ani.options(nmax = 400, 1) buffon.needle(redraw = FALSE)