continued fraction

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con·tin·ued fraction

(kən-tĭn′yo͞od)
n.
A whole number plus a fraction whose numerator is a whole number and whose denominator is a whole number plus a fraction that has a denominator consisting of a whole number plus a fraction, and so on, such as 2 + 1/(3 + 7/(1 + 2/3)).

continued fraction

n
(Mathematics) a number plus a fraction whose denominator contains a number and a fraction whose denominator contains a number and a fraction, and so on

contin′ued frac′tion


n.
a fraction whose denominator contains a fraction whose denominator contains a fraction and so on.
[1860–65]
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Noun1.continued fraction - a fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose numerator is an integer and whose denominator is an integer plus a fraction and so on
fraction - the quotient of two rational numbers
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In a previous paper [3], for any positive integer we introduced the notion of real quadratic fields with period l of minimal type (see Definition below) by using the simple continued Fraction expansions with period l of certain quadratic irrationals, and proved that there exist exactly 51 real quadratic fields of class number 1 that are not of minimal type, with one more possible exception ([3, Proposition 4.
0] = [[square root of d]] and the simple continued fraction expansion of [square root of d] is
Find the first four convergents of the simple continued fraction for [pi].

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