Irrational Number has Periodic Continued Fraction iff Quadratic

Theorem
Let $x$ be an irrational number.

Then $x$ is a quadratic irrational its continued fraction expansion is periodic.

Proof
Follows from:
 * Limit of Simple Infinite Periodic Continued Fraction is Quadratic Irrational
 * Quadratic Irrational has Periodic Continued Fraction Expansion