# This file requires specification of the number of trials (n),
# the needle length (l) and the distance between parallel lines
# (d) which should always be greater than l.
buffon=function(n,l,d) {
   win.graph()
   par(mfrow =c(2,1))
   Y <- runif(n,0,d/2)
   H <- runif(n,0,pi)
   x <- as.integer(Y < (l*sin(H))/2) 
   phat <- cumsum(x)/seq(n)
   pihat <- (2*l)/(d*phat)
   ts.plot(phat,xlab="N",ylab="Estimated Proportion",ylim=c(0,1))
   abline(h=(2*l)/(pi*d),col="red")
   title("Proportion of Crossings")
   ts.plot(pihat,xlab="N",ylab="Estimated Pi")
   title("Running Estimate of Pi")
   abline(h=pi,col="red")
   out <- list(x,pihat[n],phat[n])
   names(out) <- c("Outcomes","Pihat","Phat")
   out
}