### Some articles on *complete quotients*:

Periodic Continued Fraction - Relation To Quadratic Irrationals

... By considering the

... 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)

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