Calculating Pi using Buffon's Needle

Statistics

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.

Categorically Variable