# Compute area of quarter circle
# using random point simulation techniques

# create n random (x,y) points in square of dimension dim1
n <- 200 ; dim1 <- 750
x <- sample(0:dim1,size=n, replace=TRUE)
y <- sample(0:dim1,size=n, replace=TRUE)
x ; y

# create points (xi,y) on circle perimeter
yfunction <- c()
for (i in 1:n) {
     yfunction[i] <- sqrt(750^2 - x[i]^2)
}
yfunction
# determine which proportion of points lie within quarter circle
count1 <- 0
for (i in 1:n) {
     if(y[i] - yfunction[i] <=0) count1 <- count1 + 1
}
cat("proportion of area irrigated =", count1/n, "\n")

plot(x,y, main="picture of stochastic generated points")
points(x,yfunction)