SICP习题1.8

练习1.8 求立方根的牛顿法基于如下事实，如果y是x的立方根的一个近似值，那么下式将给出一个更好的近似值：

y=x/y2+2y3

请利用这一公式实现一个类似平方根过程的求立方根的过程。

#lang scheme;;; SICP execise 1.8 get the cube root(define (square x)  (* x x))(define (cube x)  (* x x x))(define (crt x)  (crt-iter 1.0 x))(define (crt-iter guess x);;;  (println "crt-iter");;;  (println guess);;;  (println x)  (if (guess-enough? guess (improve guess x))      (improve guess x)      (crt-iter (improve guess x) x)))(define (improve guess x)  (/ (+ (/ x (square guess)) (* 2 guess)) 3))(define (guess-enough? old-guess new-guess)  (< (/ (abs (- new-guess old-guess)) old-guess) 0.0000000001))

(crt 9)(crt 81)(crt 1000)