# Calculating Pi using Buffon’s Needle

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I put together this example to illustrate some general R programming principles for my Data Science class at iXperience. The idea is to use Buffon’s Needle to generate a stochastic estimate for pi.

> #' Exploit symmetry to limit range of centre position and angle. > #' > #' @param l needle length. > #' @param t line spacing. > #' > buffon <- function(l, t) { + # Sample the location of the needle's centre. + # + x <- runif(1, min = 0, max = t / 2) + # + # Sample angle of needle with respect to lines. + # + theta = runif(1, 0, pi / 2) + # + # Does the needle cross a line? + # + x <= l / 2 * sin(theta) + } > > L = 1 > T = 2 > # > N = 10000 > # > cross = replicate(N, buffon(L, T)) > > library(dplyr) > # > estimates = data.frame( + n = 1:N, + pi = 2 * L / T / cumsum(cross) * (1:N) + ) %>% subset(is.finite(pi))

Here are the results (click on the image for an interactive version). The orange line is the reference value and the blue line represents the results of the computation.

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