Exercise 1.35 of SICP

Exercise 1.35: Show that the golden ratio $$\phi$$ (section 1.2.2) is a fixed point of the transformation $$x\mapsto 1 + \frac{1}{x}$$, and use this fact to compute $$\phi$$ 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))

> (fixed-point (lambda (x) (+ 1 (/ 1 x))) 1.0)
1.6180327868852458


Actual value of golden ratio: 1.61803399

Tolerance: 0.0001

$$\epsilon = \left|1.61803399-1.6180327868852458\right| = .0000012031147542 < 0.0001$$

Clearly $$\epsilon$$ is in the defined error tolerance.