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I came across this post which gives a method to estimate Pi by using a circle, it’s circumscribed square and (lots of) random points within said square. Booth used Stata to estimate Pi, but here’s some R code to do the same thing…

x <- 0.5 # center x y <- 0.5 # center y n <- 1000 # nr of pts r <- 0.5 # radius pts <- seq(0, 2 * pi, length.out = n) plot(sin(pts), cos(pts), type = 'l', asp = 1) # test require(sp) xy <- cbind(x + r * sin(pts), y + r * cos(pts)) sl <- SpatialPolygons(list(Polygons(list(Polygon(xy)), "polygon"))) plot(sl, add=FALSE, col = 'red', axes=T ) # the square xy <- cbind(c(0, 1, 1, 0), c(0, 0, 1, 1)) sq <- SpatialPolygons(list(Polygons(list(Polygon(xy)), "polygon"))) plot(sq, add = TRUE) N <- 1e6 x <- runif(N, 0, 1) y <- runif(N, 0, 1) sp <- SpatialPoints(cbind(x, y)) plot(sp, add = TRUE, col = "green") require(rgeos) (sim_pi <- (sum(gIntersects(sp, sl, byid = TRUE))/N) *4) sim_pi - pi

Note the use of sp and rgeos packages to calculate the intersections.

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