**Exercise 1.35:** Show that the golden ratio \( \phi \) (section 1.2.2) is a fixed point of the transformation
\( x\mapsto 1 + \frac{1}{x} \), and use this fact to compute \( \phi \) by means of the `fixed-point`

procedure.

```
(define tolerance 0.00001)
(define (fixed-point f first-guess)
(define (close-enough? v1 v2)
(< (abs (- v1 v2)) tolerance))
(define (try guess)
(let ((next (f guess)))
(if (close-enough? guess next)
next
(try next))))
(try first-guess))
```

```
> (fixed-point (lambda (x) (+ 1 (/ 1 x))) 1.0)
1.6180327868852458
```

Actual value of golden ratio: 1.61803399

Tolerance: 0.0001

$$ \epsilon = \left|1.61803399-1.6180327868852458\right| = .0000012031147542 < 0.0001 $$

Clearly \( \epsilon \) is in the defined error tolerance.