pi.greco2=function(nrepl=10000){
 somma = 0
    for(i in 1:nrepl){
    x=runif(1, min=0, max=1)
    somma= somma + 1/sqrt(1 -x^2)
        }
    return( 2*somma/nrepl )
}

=====================================

pi.greco=function(nrepl=10000){
xy=runif(nrepl*2, min=-1, max=1)
dim(xy)=c(nrepl,2)
inside=apply(xy^2,1,sum)<1
plot(xy, pch=20, cex=.5, col=c("navy","pink")[inside+1],
xlab="x", ylab="y", main=paste("nrepl =",nrepl))
a=seq(0,2*pi,length.out=100)
xy.circle=cbind(cos(a),sin(a))
lines(xy.circle,col="pink",lwd=2)
return( sum(inside)/nrepl *4)
}

============================================

pi.greco6 = function(nrepl=10000){
        x=runif(nrepl, min=0, max=0.5)
        dim(x) = c(nrepl,1)
        somma= sum(1/sqrt(1 -x^2),1)
        print(somma*3/nrepl)
    }


===================================


 nepero = function(nrepl=10){
     sommatoria = 0
     for(i in 1:nrepl){
         somma=0
         passi=0
         while(somma<1){
             x = runif(1,min=0,max=1)
             somma= somma + x
             passi = passi +1
         }
         sommatoria = sommatoria + passi 
         numero = sommatoria/nrepl
     }
     return(numero)
 }