Monte Carlo calculation of Pi

monte-carlo-pi.clj

(ns mc.core
  (:use [clojure.contrib.seq-utils :only [separate]]))

; http://math.fullerton.edu/mathews/n2003/MonteCarloPiMod.html

(defn- square [x]
  (* x x))

(defn- distance [[x y]]
  (Math/sqrt (+ (square x)
		(square y))))

(defn- point
  ([] (point (rand) (rand)))
  ([x y] (vector x y)))

(defn- in-circle? [point]
  (< (distance point) 1))

(defn- points []
  (lazy-seq (cons (point) (points))))

(defn monte-carlo-pi [n]
  (let [[in out] (separate in-circle? (take n (points)))]
    (double (* 4 (/ (count in) (+ (count in) (count out)))))))

; > (monte-carlo-pi 100000)
; 3.14456