From: Ramakrishnan Muthukrishnan Date: Mon, 10 May 2010 17:19:03 +0000 (+0530) Subject: solution to 1.35 X-Git-Url: https://git.rkrishnan.org/components/com_hotproperty/%22doc.html/statistics?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 +)