In today’s Programming Praxis exercise, our goal is to approximate pi by using Georges-Louis Leclerc’s method of dropping needles on a board. Let’s get started, shall we?
import Control.Applicative import System.Random
We're going to be needing two sets of random numbers; one for the position and one for the angle of the needles. In order to save some code and to stop Haskell complaining about ambiguous types we make a function to generate an infinite amount of numbers in the [0,1) range.
rnds :: IO [Double] rnds = fmap randoms newStdGen
We approximate pi by dividing the total amount of needles dropped by the number of needles that hit a line.
buffon :: Int -> IO Double buffon n = (fromIntegral n /) . sum . take n <$> (zipWith (\y t -> if y < sin (t*pi/2) / 2 then 1 else 0) <$> rnds <*> rnds)
Running the simulation reveals that this isn't a very practical way of approximating pi: after one million needles it generally only has two correct digits.
main :: IO () main = print =<< buffon 1000000