From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Mon, 10 May 2010 17:19:03 +0000 (+0530)
Subject: solution to 1.35
X-Git-Url: https://git.rkrishnan.org/%5B/frontends/%22news.html//%22%22.?a=commitdiff_plain;h=a8d525bc98c353a8bddc13659cc3a28c14a05c70;p=sicp.git

solution to 1.35
---

diff --git a/src/sicp/ex1_35.clj b/src/sicp/ex1_35.clj
new file mode 100644
index 0000000..35094e6
--- /dev/null
+++ 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
+)