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
A fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose denominator is an integer plus a fraction - and so on to an infinite number of terms.
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction, the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression. In either case, all integers in the sequence, other than the first, must be positive. The integers ai are called the coefficients or terms of the continued fraction. Continued fractions have a number of remarkable properties related to the Euclidean algorithm for integers or real numbers. Every rational number pq has two closely related expressions as a finite continued fraction, whose coefficients ai can be determined by applying the Euclidean algorithm to. The numerical value of an infinite continued fraction will be irrational; it is defined from its infinite sequence of integers as the limit of a sequence of values for finite continued fractions. Each finite continued fraction of the sequence is obtained by using a finite prefix of the infinite continued fraction's defining sequence of integers. Moreover, every irrational number α is the value of a unique infinite continued fraction, whose coefficients can be found using the non-terminating version of the Euclidean algorithm applied to the incommensurable values α and 1. This way of expressing real numbers is called their continued fraction representation.
The numerical value of continued fraction in Chaldean Numerology is: 8
The numerical value of continued fraction in Pythagorean Numerology is: 2
Images & Illustrations of continued fraction
Translations for continued fraction
From our Multilingual Translation Dictionary
Get even more translations for continued fraction »
Find a translation for the continued fraction definition in other languages:
Select another language:
Discuss these continued fraction definitions with the community:
Word of the Day
Would you like us to send you a FREE new word definition delivered to your inbox daily?
Use the citation below to add this definition to your bibliography:
"continued fraction." Definitions.net. STANDS4 LLC, 2018. Web. 26 Apr. 2018. <https://www.definitions.net/definition/continued fraction>.