(require 'stdlib)

(define boardsize 1000)

(define (in-circle-p coord radius)
  (let ((x (car coord)) (y (cdr coord)))
    (<= (+ (* x x) (* y y)) (* radius radius))))

(define (generate-sample)
  (define (one-sample)
    (- (random boardsize) (/ boardsize 2)))
  (cons (one-sample) (one-sample)))

(define (do-n-samples n)
  (let ((in 0) (out 0))
    (dotimes i n
             (if (in-circle-p (generate-sample) (/ boardsize 2))
                 (setq in (1+ in))
               (setq out (1+ out))))
    (cons in out)))

;; stel radius 1,
;; oppervlakte vierkant = 2 * 2 = 4
;; oppervlakte circel = PI * 1^2 = PI
;; verhouding oppervlakte circel : vierkant = PI : 4
;; verhouding samples in : totaal = PI : 4
;; PI = 4 * in/N

(define (approx-pi n)
  (let ((result (do-n-samples n)))
    (exact->inexact (* 4 (/ (car result) n)))))