From a8d525bc98c353a8bddc13659cc3a28c14a05c70 Mon Sep 17 00:00:00 2001 From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com> Date: Mon, 10 May 2010 22:49:03 +0530 Subject: [PATCH] solution to 1.35 --- src/sicp/ex1_35.clj | 21 +++++++++++++++++++++ 1 file changed, 21 insertions(+) create mode 100644 src/sicp/ex1_35.clj 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 +) -- 2.45.2