Monte Carlo Pi esitmation

# estimating Pi using simple Monte Carlo Metod
# method: http://en.wikipedia.org/wiki/Monte_Carlo_method
# blog: http://reakt.com

library(plotrix)
library(grid)

# distance between points 'x' and 'y'
distance <- function(x,y) {

  n <- length(x)

  if (n!=length(y)) stop("Different X and Y dimensions.")

  sqrt(sum(sapply(1:n, function(i) (x[i]-y[i])^2)))

}

# number of points drawn
n <- 1000

x <- runif(n,0,1)
y <- runif(n,0,1)

# plot points and circle
plot(x,y,type="p",pch=16,asp=1)
draw.circle( 0, 0, 1 )

# distance between points and the center of the circle
d <- sapply(1:n, function(i) distance(c(0,0),c(x[i],y[i])))

# proportion of points inside the circle * 4 -> pi
pi.mc <- length(which(d<=1))/n*4

points(x[which(d<=1)],y[which(d<=1)],col="Red",pch=16)

# Monte Carlo Pi estimation:
pi.mc