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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

© 1996-9 Eric W. Weisstein