Quadratic Irrational Number

An Irrational Number of the form

$${P\pm \sqrt{D}\over Q},$$

where $P$ and $Q$ are Integers and $D$ is a Squarefree Integer. Quadratic irrational numbers are sometimes also called Quadratic Surds. In 1770, Lagrange proved that that any quadratic irrational has a Continued Fraction which is periodic after some point.

See also Continued Fraction, Quadratic Surd