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 ...
... 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 (18441900)
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