# Definition of Continued fraction. Meaning of Continued fraction. Synonyms of Continued fraction

Here you will find one or more explanations in English for the word Continued fraction. Also in the bottom left of the page several parts of wikipedia pages related to the word Continued fraction and, of course, Continued fraction synonyms and on the right images related to the word Continued fraction.

## Definition of Continued fraction

Continued fraction
Fraction Frac"tion, n. [F. fraction, L. fractio a breaking, fr. frangere, fractum, to break. See Break.] 1. The act of breaking, or state of being broken, especially by violence. [Obs.] Neither can the natural body of Christ be subject to any fraction or breaking up. --Foxe. 2. A portion; a fragment. Some niggard fractions of an hour. --Tennyson. 3. (Arith. or Alg.) One or more aliquot parts of a unit or whole number; an expression for a definite portion of a unit or magnitude. Common, or Vulgar, fraction, a fraction in which the number of equal parts into which the integer is supposed to be divided is indicated by figures or letters, called the denominator, written below a line, over which is the numerator, indicating the number of these parts included in the fraction; as 1/2, one half, 2/5, two fifths. Complex fraction, a fraction having a fraction or mixed number in the numerator or denominator, or in both. --Davies & Peck. Compound fraction, a fraction of a fraction; two or more fractions connected by of. Continued fraction, Decimal fraction, Partial fraction, etc. See under Continued, Decimal, Partial, etc. Improper fraction, a fraction in which the numerator is greater than the denominator. Proper fraction, a fraction in which the numerator is less than the denominator.
Continued fraction
Continued Con*tin"ued, p. p. & a. Having extension of time, space, order of events, exertion of energy, etc.; extended; protracted; uninterrupted; also, resumed after interruption; extending through a succession of issues, session, etc.; as, a continued story. ``Continued woe.' --Jenyns. ``Continued succession.' --Locke. Continued bass (Mus.), a bass continued through an entire piece of music, while the other parts of the harmony are indicated by figures beneath the bass; the same as thorough bass or figured bass; basso continuo. [It.] Continued fever (Med.), a fever which presents no interruption in its course. Continued fraction (Math.), a fraction whose numerator is 1, and whose denominator is a whole number plus a fraction whose numerator is 1 and whose denominator is a whole number, plus a fraction, and so on. Continued proportion (Math.), a proportion composed of two or more equal ratios, in which the consequent of each preceding ratio is the same with the antecedent of the following one; as, 4 : 8 : 8 : 16 :: 16 : 32.

## Meaning of Continued fraction from wikipedia

- Examples of finite simple continued fractions Formula Numeric Remarks   a 0 {\displaystyle \ a_{0}}   2 {\displaystyle \ 2} All integers are a degenerate...
- a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial...
- In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning...
- A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English,...
- In mathematics, an infinite periodic continued fraction is a continued fraction that can be placed in the form x = a 0 + 1 a 1 + 1 a 2 + ⋱ ⋱ a k + 1 a...
- irrational. Therefore, π cannot have a periodic continued fraction. Although the simple continued fraction for π (shown above) also does not exhibit any...
- The Rogers–Ramanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related...
- a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since...
- {\displaystyle b\neq k} . It is also disjunctive sequence. The simple continued fraction expansion of Champernowne's constant has been studied as well. Kurt...
- continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction...