Calculating Pi using Buffon’s Needle

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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