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)