ex_1_35.rkt

#lang racket

;fi^2 = fi + 1
;fi^2 - fi = 1
;fi(fi - 1) = 1
;fi - 1 = 1/fi
;fi = 1 + 1/fi

(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))

(fixed-point (lambda (x) (+ 1 (/ 1 x)))
             1.0)