Estimate Pi With Monte Carlo

Estimate Pi With Monte Carlo

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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Example Using R

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:

[1] 3.14204

python pi probability monte-carlo-simulation rstats

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