1.35|

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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)