1 ;;; show that golden ratio, phi, is a fixed point of the transformation x -> 1 + 1/x
2 ;;; and use this fact to compute phi by means of the fixed point procedure.
5 (:use [sicp utils ch1_3]
6 [clojure.contrib test-is]))
8 ;;; the fixed point of the transformation x-> 1 + 1/x is the same as
9 ;;; root of x - 1 - 1/x = 0 or x^2 - x - 1 = 0
11 ;;; using the half-interval-method, (and knowing that phi is 1.61...)
13 (half-interval-method (fn [x] (- (* x x) x 1)) 1.0 2.0)
19 (fixed-point (fn [x] (+ 1 (/ 1 x))) 1.0)
20 ;;;=> 1.6180327868852458