Lagrange's continued fraction theorem, proved by Lagrange in 1770, states that any positive quadratic surd 
has a regular
continued fraction which is periodic
after some point.
Lagrange's Continued Fraction Theorem
See also
Periodic Continued Fraction, Quadratic Surd, Regular Continued FractionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Lagrange's Continued Fraction Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LagrangesContinuedFractionTheorem.html