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Problem 1.35
Friday, August 23, 2019; ago; Download .md

SICP Exercise 1.35

Given:

$$ x \leftarrow 1 + \frac{1}{x} $$

Multiply by $$x$$ on both sides:

$$ x^2 \leftarrow x + 1 $$

Which is the defination of $$\phi$$ from 1.2.2. Now solving the quadratic gives:

$$ \phi = \frac{1 + \sqrt{5}}{2} \approx 1.6180 $$

Using fixed-point to calculate this:

(fixed-point (lambda (x) (+ 1 (/ 1 x))) 1.0)