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(This article was first published on <strong><a href="http://www.exegetic.biz/blog/2016/07/calculating-pi-using-buffons-needle/"> R – Exegetic Analytics</a></strong>, and kindly contributed to <a rel="nofollow" href="http://www.r-bloggers.com/">R-bloggers)</a> </div>
<p>I put together this example to illustrate some general R programming principles for my Data Science class at <a target="_blank" href="http://ixperience.co.za/">iXperience</a>. The idea is to use <a target="_blank" href="https://en.wikipedia.org/wiki/Buffon%27s_needle">Buffon’s Needle</a> to generate a stochastic estimate for pi.</p>
<pre>
> #' Exploit symmetry to limit range of centre position and angle.
> #' 
> #' @param l needle length.
> #' @param t line spacing.
> #' 
> buffon &lt;- function(l, t) {
+   # Sample the location of the needle's centre.
+   #
+   x &lt;- 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 &lt;= 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))
</pre>
<p>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.</p>
<p><a target="_blank" href="https://plot.ly/~collierab/461/estimating-pi-using-buffons-needle/"><img sizes="(max-width: 798px) 100vw, 798px" srcset="http://i2.wp.com/www.exegetic.biz/blog/wp-content/uploads/2016/07/buffon-needle-pi.png?resize=456%2C227 798w, http://www.exegetic.biz/blog/wp-content/uploads/2016/07/buffon-needle-pi-624x311.png 624w" alt="Estimating pi with Buffon's Needle" class="wp-image-3791" src="http://i2.wp.com/www.exegetic.biz/blog/wp-content/uploads/2016/07/buffon-needle-pi.png?resize=456%2C227" data-recalc-dims="1"></a></p>
<p>The post <a target="_blank" rel="nofollow" href="http://www.exegetic.biz/blog/2016/07/calculating-pi-using-buffons-needle/">Calculating Pi using Buffon’s Needle</a> appeared first on <a target="_blank" rel="nofollow" href="http://www.exegetic.biz/blog">Exegetic Analytics</a>.</p>
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