1.8 Exercise 1.8

To make this exercise more interesting, I’ve written an iteration procedure which takes an improve function as an argument. This means that the only difference between a procedure computing square roots and a procedure computing cube roots is the choice of improvement function. This generalization is handled differently later in the chapter.

(I use my previously-defined good-enough? procedure with a good-enough-factor of 0.001.)

(define (cube-root x)   (root-iter x 1.0 0.0 cube-root-improve))

(define (root-iter x guess previous-guess improve)   (if (good-enough? guess previous-guess) guess       (root-iter x (improve guess x) guess improve)))

(define (cube-root-improve x guess)   (/    (+     (/ x (* guess guess))     (* 2 guess))    3))