求平方根

SUCCESSIVE AVERAGING DUE TO HERON OF ALEXANDRIA
** TO FIND AN APPROXIMATION TO SQRT(X) **

1. MAKR A GUESS G
2. IMPROVE THE GUESS BY AVERAGING G AND X/G
3. KEEP IMPROVING THE GUESS UNTILE IT IS GOOD ENOUGH

4. USE 1 AS AN INITIAL GUESS

   算法思想

   (define (try guess x)
   (if (good-enough? guess x)
       guess
       (try (improve guess x) x)))
   (define (sqrt x) (try 1 x))

   参考代码

   注：此代码来自https://blog.csdn.net/jazz_charles/article/details/48974029

   (define (square x) (* x x)) //定义求平方  
   (define (average x y) (/ (+ x y) 2)) //定义求平均值  
   (define (sqrt x) //定义求平方根  
     (define (accurate guess) //定义判断精确度  
          (<   (abs (-  (square guess)  x)) 0.001))  
     (define (improve guess) //定义改进近似值  
         (average x  (/ x guess)))  
     (define (sqrt-iter guess) //定义主体迭代求解  
         (if   (accurate guess)  
                guess  
               (sqrt-iter (improve guess))))  
     (sqrt-iter 1.0))