Golden ratio

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


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(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))


(check-equal? (round (* 10000 (fixed-point solution 1.0))) 16180.0)