solution to 1.35

diff --git a/src/sicp/ex1_35.clj b/src/sicp/ex1_35.clj
new file mode 100644 (file)
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+++ b/src/sicp/ex1_35.clj
@@ -0,0 +1,21 @@
+;;; show that golden ratio, phi, is a fixed point of the transformation x -> 1 + 1/x
+;;; and use this fact to compute phi by means of the fixed point procedure.
+
+(ns sicp.ex1_35
+  (:use [sicp utils ch1_3]
+       [clojure.contrib test-is]))
+
+;;; the fixed point of the transformation x-> 1 + 1/x is the same as
+;;; root of x - 1 - 1/x = 0 or x^2 - x - 1 = 0
+;;
+;;; using the half-interval-method, (and knowing that phi is 1.61...)
+(comment
+(half-interval-method (fn [x] (- (* x x) x 1)) 1.0 2.0)
+;;;=>  1.61767578125
+)
+
+;;; using fixed point
+(comment
+(fixed-point (fn [x] (+ 1 (/ 1 x))) 1.0)
+;;;=> 1.6180327868852458
+)