Complete Quotients

Some articles on complete quotients:

Periodic Continued Fraction - Relation To Quadratic Irrationals
... By considering the complete quotients of periodic continued fractions, Euler was able to prove that if x is a regular periodic continued fraction, then x is a quadratic irrational number ... discriminant, that relate the successive complete quotients of the regular continued fraction expansion of x to one another ... of these equations (the coefficients are bounded), the complete quotients (and also the partial denominators) in the regular continued fraction that represents x must eventually repeat ...

Famous quotes containing the word complete:

    We place no particular value upon the possession of a virtue until we detect its complete absence in our adversary.
    Friedrich Nietzsche (1844–1900)