sicp exercise 1.35

;  Exercise 1.35. Show that the golden ratio (section 1.2.2) is a fixed point of the transformation
;  x --> 1 + 1/x, and use this fact to compute by means of the fixed-point procedure.


(define tolerance 0.00001)
(define (fixed-point f first-guess)
   (define (close-enough? v1 v2)
      (< (abs (- v1 v2)) tolerance))
   (define (try guess)
      (let ((next (f guess)))
        (if (close-enough? guess next)
            next
            (try next))))
   (try first-guess))

(define (phi x) (+ 1 (/ 1 x)))

(display (rationalize(fixed-point phi 1) 0.0001)) (newline)