因为找不到SICP的辅导书, 有些要求explain的solution就不知道答案了, sigh...
不知道直接去找MIT的教授要, 他们会不会给...

1.1.7 Square Roots by Newton's Method
(define (avg x y)
  (/ (+ x y) 2))

(define (abs x)
  (if (< x 0)
      (- x)
      x))

(define (IsGoodEnough? guess target)
   (< (abs (- (* guess guess) target)) 0.00000000000000001))

     (define (improve guess target)
  (avg (/ target guess) guess))

(define (sqrt-iter guess target)
  (if (ISGoodEnough? guess target)
      guess
      (sqrt-iter (improve guess target)
                 target)))

(define (sqrt x)
  (sqrt-iter 1.0 x))

(define (new-if predicate then-clause else-clause)
  (cond (predicate then-clause)
        (else else-clause)))

(define (new-sqrt-iter guess target)
  (new-if (ISGoodEnough? guess target)
      guess
      (new-sqrt-iter (improve guess target)
                 target)))

(define (new-sqrt x)
  (new-sqrt-iter 1.0 x))

Exercise 1.8: Newton’s method for cube roots is based on the fact that if y is
an approximation to the cube root of x, then a better approximation is given
b y the value
x/y^2 + 2y
----------
3
Use this formula to implement a cube-root procedure analogous to the squareroot procedure. (In section Section 1.3.4 [1-3-4], page 69 we will see how to implement Newton’s method in general as an abstraction of these square-root and cube-root procedures.)
section 1.3.4 we will see how to implement Newton's method in general as an abstraction of these square-root and cube-root procedures.)

My Solution:

(define squre
  (lambda (x)
    (* x x)))

(define abs
  (lambda (x)
    (if (< x 0)
        (- x)
        x)))

(define cube
  (lambda (x)
    (* x x x)))

(define IsGoodEnough?
  (lambda (guess target)
    (< (abs (- (cube guess) target)) 0.0000000000001)))

     (define improve
  (lambda (guess target)
    (/ (+ (/ target (squre guess)) (* 2 guess)) 3)))

(define cube-iter
  (lambda (guess target)
    (if (isGoodEnough? guess target)
        guess
        (cube-iter (improve guess target) target))))
(define cube-root
  (lambda (n)
    (cube-iter 1.0 n)))

(cube-root 8)
(cube-root 27)
(cube-root 3)
(cube-root 2)