3.5

;3.5
(define (estimate-pi trails)
  (sqrt (/ 6 (monte-carlo trails experiment))))

(define (random-in-range low high)
  (let ((range (- high low)))
    (+ low (random (+ 1 range)))));sicp 中为说明 random是获得 0 - (range-1)的一个数 难怪用sicp的 random-in-range总是错

(define (monte-carlo trails experiment)
  (define (iter remain res)
    (cond ((= 0  remain) (/ res trails))
          ((experiment)
           (iter (- remain 1) (+ 1 res)))
          (else (iter (- remain 1) res))))
  (iter trails 0))

(define (fractional trails x1 x2 y1 y2 p)
  (define (test-func) 
     (p x1 x2 y1 y2))
  (* (* (- x2 x1) (- y2 y1)) (monte-carlo trails test-func)))

(define (test-func x1 x2 y1 y2)
  (< (+ (square (random-in-range x1 x2))
        (square (random-in-range y1 y2)))
     1))
  
(define (p x1 x2 y1 y2)
  (< (+ (square (random-in-range x1 x2))
        (square (random-in-range y1 y2)))
     1))

(define the-pi 
  (lambda (trails x1 x2 y1 y2 p)
    (fractional trails x1 x2 y1 y2 p)
       ))

(define (square x) (* x x))