1.35, 1.36 sicp

fixed-point.scm

(define tolerance 0.00001)

(define (close-enough? v1 v2)
  (< (abs (- v1 v2)) tolerance))

(define (fixed-point f first-guess)
  (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) ; 1.6180327868852458

(define (dampened-fixed-point f first-guess)
  (define (try guess)
    (let ((next (/ (+ guess (f guess)) 2)))
      (if (close-enough? guess next)
	  next
	  (try next))))
  (try first-guess))


(define (func x) (/ (log 1000) (log x)))

(fixed-point func 2.0)
(dampened-fixed-point (lambda (x) (/ (log 1000) (log x))) 2.0)