1.31 (另一种求圆周率的算法)

Posted 2020-10-15 ...............洋葱的秋秋空间........

(define (product term a next b)
  (if (> a b)
      1
      (* (term a)
         (product term (next a) next b))))

(product (lambda (x) x)
         1
         (lambda (i) (+ i 1))
         5)

　　

(define (product term a next b)
  (define (iter a result)
    (if (> a b)
        result
        (iter (next a)
              (* (term a) result))))
  (iter a 1))

(define (product-normal term a next b)
  (if (> a b)
      1
      (* (term a)
         (product term (next a) next b))))

(define (factorial n)
  (product (lambda (x) x)
           1
           (lambda (i) (+ i 1))
           n))

(define (numer-term i)
  (cond ((= i 1) 2)
        ((even? i) (+ i 2))
        (else (+ i 1))))

(define (denom-term i)
  (if (odd? i)
      (+ i 2)
      (+ i 1)))

(define (pi n)
  (* 4
     (exact->inexact ; exact->inexact 函数转换除法的商,确保计算所得的结果为浮点数格式(而不是分数格式)
        (/ (product numer-term
                    1
                    (lambda (i) (+ i 1))
                    n)
           (product denom-term
                    1
                    (lambda (i) (+ i 1))
                    n)))))

(pi 50000)