Approximate pi using Archimedes' method

archimedes.hs

module Main (main) where

import Control.Monad (forM_)

-- | Given the length l of a cord from points A to B on the unit circle, compute
-- the length of the cords A-C and C-B, where C is the point on the unit circle
-- exactly in between A and B.
iterArchimedes :: Double -> Double
iterArchimedes l = l / sqrt (2 + sqrt (4 - l*l))

main :: IO ()
main =
  forM_ (zip [0..1000] (iterate iterArchimedes 2)) $ \(n, b_twotothen) ->
    let bb_twotothen = 2^n * b_twotothen
    in putStrLn ("n=" ++ show n ++ ", b_{2^n} = " ++ show b_twotothen ++ ", B_{2^n} = " ++ show bb_twotothen)