Function gives numeric(0) for every input

Hi,

I am trying to code buffons needle in R for a class

This is my code w/ output from R, if anyone could tell me why this is
happening it would be amazing,

I can generate correct results without putting the steps into a function but
alas that is the assignment.

buffon = function(n){

+ x = NULL
+ theta = NULL
+ a = NULL
+ phat = numeric(0)
+ i = 1
+ 
+ while ( i <= n){
+ x[i] <- runif(1,0,1/2)
+ theta[i] <- runif(1,0,pi/2)
+ a[i] <- 1/2 * (sin(theta[i])) - x[i] 
+ 
+ 
+ if (a[i] <= 0)phat <- phat + 1
+ else phat<-phat
+ i <- i + 1
+ 
+  }
+ return(phat)
+ }

buffon(10)

numeric(0)

Thanks Again

the response should be the number of times a[i] is less than or equal to
zero, which i am calling phat

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