con·tin·ued fraction

(kən-tĭn′yo͞od)

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)).

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

continued fraction

(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

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

contin′ued frac′tion

a fraction whose denominator contains a fraction whose denominator contains a fraction and so on.

[1860–65]

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Noun

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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fraction

References in periodicals archive

Any finite continued fraction represents a rational number [8].

Global Scaling of Planetary Atmospheres

Then, expanding (3) into a continued fraction by the Euclidean algorithm, we obtain the block diagram of the regulator shown in Fig.

STABILITY AND ACCURACY OF THE ROBUST SYSTEM FOR STABILIZING THE ROTOR FLUX-LINKAGE OF AN ASYNCHRONOUS ELECTRIC DRIVE AT RANDOM VARIATIONS OF THE UNCERTAIN PARAMETERS WITHIN THE SPECIFIED BOUNDARIES

This, together with the fact that well-approximations come from the continued fraction, allows us to arrive at our desired estimate.

A note on transcendental entire functions mapping uncountable many Liouville numbers into the set of Liouville numbers

We give 2-, 4-, 8- and 16-dissections of a continued fraction of order sixteen.

On the expansion of Ramanujan's continued fraction of order sixteen

As in the classical context of real numbers, we have a continued fraction algorithm in K(([X.sup.-1])).

On the approximation exponent of some hyperquadratic power series

This section presents the method of synthesizing the distribution of characteristics on a continued fraction making it possible to obtain the parameters and the model of a single-axis system.

Active reduction of identified machine drive system vibrations in the form of multi-stage gear units/Masinu pavaroje nustatytu mechaniniu virpesiu aktyvus slopinimas daugiapakopese krumpliaratinese pavarose

We will be concerned with the simple continued fraction expansions of [square root of D] where D is an integer that is not perfect square.

Counterexamples to a theorem concerning solution of certain quadratic Diophantine equation

The simple and pretty continued fraction expression suggests that there might be other pretty formulae involving [square root of 2].

The square root of 2

It has also been stated in terms of a continued fraction by Read [Rea79], so that the Touchard-Riordan formula is:

Touchard-Riordan formulas, T-fractions, and Jacobi's triple product identity

The set of all paths (a formal language) is given by the infinite continued fraction

Continued fraction expansions for q-tangent and q-cotangent functions

Among several methods, continued fraction is one of the techniques that is used to obtain transient solution.

M/M/1 queue with feedback a continued fraction approach