Project Euler Problem 57 was a little too easy, not even taking 15 minutes to write and test. Even then, I spent the majority of my time staring at the recursive form of the expansion of `sqrt(2)`

until I saw how to write it as an infinite sequence. (A pen and paper may help you figure it out.)

```
(def sqrt2-approx (iterate #(/ (+ (numerator %) (* 2 (denominator %)))
(+ (numerator %) (denominator %)))
(/ 3 2)))
(defn bigger-numerator? [n]
(> (count (str (numerator n)))
(count (str (denominator n)))))
(defn euler-57 []
(count (filter bigger-numerator? (take 1000 sqrt2-approx))))
(time (euler-57)) ;; "Elapsed time: 144.948143 msecs"
```

Using Clojure’s fractional types here lets us avoid some of the syntactic noise that using separate denominator and numerator fields, multiple return arguments, destructuring the arguments would require.

Ciao!