Pi Finder Manual

In recognition of just having passed pi day (March 14: 3-14), I produced a pi calculator using Monte Carlo simulation. It is visible at https://pbulsink.shinyapps.io/pi_finder/, and will be explained in the next slides.

Mathematical Background

You can simulate the value of pi by repeatedly plotting points with randomly selected x and y values, then calculating the distance from that point to the origin (at [0,0]). The distance of that point to the origin is \( d = sqrt(x^2+y^2) \). Multiplying the number of points where distance to the origin is one or less by 4 will give you an approximately calculated simulation of pi.

A point is plotted on a chart with \( x= \) runif() and \( y= \) 'runif()'.

x <- runif(1); y <- runif(1)
d <- sqrt(x^2 + y^2)

In this example, \( x= \) 0.876, and \( y= \) 0.595, so then \( d= \) 1.059.

So, for n repeats, where \( n = 10 000 \):

n <- 10000; x <- runif(n); y <- runif(n)
d <- sqrt(x^2 + y^2)
in_pi <- ifelse(d<=1, TRUE, FALSE)
est_pi <- 4 * sum(in_pi)/n

We get an estimate of pi to be 3.1584. Not bad!