Monte Carlo Method in R

Question

I'm trying to learn R. I'm trying to write a program which calculates (approximately) pi. Read About the method

My code is not working right now!

f <- 0
s <- 0
range <- 10000
for (i in (1:range)) {
    v <- sample(1:range, 1)/range
    n <- sample(1:range, 1)/range

    if ( sqrt (v*v + n*n) <= 1) {
        f <- f + 1
    } else if ( v <=1 && n <= 1) {
        s <- s+1
    }
}

print ( f/s )

Answer 1

Here's an improved version of your code

range = 100000
v = runif(range)
n = runif(range)
f = sum(sqrt(v^2 + n^2) <= 1)

print(4 * f / range)

You should use runif to get samples from a uniform instead of sample(...) / range.

The s is unnecessary since what you're doing is counting the number of times, f, that your random point (v,n) is within the circle in that quadrant, divided by the number of attempted draws, which would just be range in your case.

You need to multiply by 4 since f / range approximates the area of one-quarter of the unit circle.