# Project Euler Problem 57

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!