介绍

rneedle <- function(n) {
  x = runif(n, 0, 5) 
  y = runif(n,0, 1)
  angle = runif(n,-pi, pi) #angle from -180 to 180 
  values<-data.frame(cbind(x, y, angle))
  return(values)
}
values<-rneedle(50)
#check that a 50 by 3 matrix is generated 

values
#Our dataframe has been successfully produced.

            x           y      angle
1  4.45796267 0.312440618  1.3718465
2  3.43869230 0.462824677  2.9738367
3  2.55561523 0.596722445 -2.9638285
4  3.68098572 0.670877506 -0.6860502
5  0.03690118 0.202724803 -0.3315141
6  4.64979938 0.180091416 -0.3293093
7  4.92459238 0.172328845 -0.5221133
8  3.50660347 0.752147374  2.9100221
9  2.03787919 0.167897415 -0.3213833
10 0.38647133 0.539615776 -0.1188982
11 3.28149935 0.102886770 -1.6318256
12 3.68811892 0.765077533  1.2459037
13 1.52004894 0.682455494 -0.4219802
14 3.76151379 0.508555610  0.1082087
...

plotneedle(values)

buffon(values) 

set.seed(10312013)
X <- rneedle(50)
plotneedle(X)
buffon(X)

> buffon(X)
[1] 3.846154

Approxpi(500)
mean(Approxpi(500)) 
var(Approxpi(500)) 

> mean(Approxpi(500)) 
[1] 3.172314
> var(Approxpi(500)) 
[1] 0.04751391