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continued fraction

American  

noun

Mathematics.
  1. a fraction whose denominator contains a fraction whose denominator contains a fraction, and so on.


continued fraction British  

noun

  1. 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 & Unabridged" 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Etymology

Origin of continued fraction

First recorded in 1860–65

Example Sentences

Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.

See Examples For:

These latest projects are primarily driven by a specific continued fraction whose nested integers form the sequence 1, 2, 3,…, Elsner says.

From Scientific American Jun. 2, 2023

The Convergence of Infinite Continued Fractions.—We have seen that the simple infinite continued fraction converges.

From Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 2 "Constantine Pavlovich" to "Convention" by Various

It easily follows that the continued fraction is incommensurable if a/b, c/d, etc., being at first greater than unity, become and continue less than unity after some one point.

From A Budget of Paradoxes, Volume II by Smith, David Eugene

The simple continued fraction is both the most interesting and important kind of continued fraction.

From Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 2 "Constantine Pavlovich" to "Convention" by Various

He had not then the continued fraction, a mode of representation which he gave the next year in his work on the square root.

From A Budget of Paradoxes, Volume I by Smith, David Eugene

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