Estimate Pi With Monte Carlo. Example of how you can estimate Pi With Monte Carlo in four lines of code
One method to estimate the value of π is by applying the Monte Carlo method. Let’s consider a circle inscribed in a square. Then for a radius r, we have:
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Below, we represent how we can apply the Monte Carlo Method in R to estimate the π.
## set the seed for reproducility set.seed(5) ## number of simulations n=1000000 ## generate the x1 and x2 co-ordinates from uniform ## distribution taking values from -1 to 1 x1<-runif(n, min=-1, max=1) x2<-runif(n, min=-1, max=1) ## Distrance of the points from the center (0,0) z<-sqrt(x1^2+x2^2) ## the area within the circle is all the z ## which are smaller than the radius^2 ## in our case radius=1 4*sum((z<=1))/length(z)
And we get:
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