SICP exercise 1.35

From Drewiki

Problem

Show that the golden ratio $\phi\,$ (see section 1.2.2 of the text) is a fixed point of the transformation $x \mapsto 1 + 1/x$ , and use this fact to compute $\phi\,$ by means of the fixed-point procedure.

Solution

The fixed point of the function is

$1 + 1/x = x\,$

Solving for x, we get

$x^2 = x + 1\,$

$x^2 - x - 1 = 0\,$

Using the quadratic equation to solve for x, we find that one of the roots of this equation is $\frac{1 + \sqrt{5}}{2}$ , which is the golden ratio $\phi\,$ (approximately 1.6.18).

Using the fixed-point procedure from the text to compute the numeric value:

The result produced by Chicken Scheme 3.1 on Mac OS X 10.5 on a MacBook Pro is

SICP exercise 1.35

From Drewiki

Problem

Solution

Views

Personal tools

Navigation

Search

Toolbox