continued fraction

American  

noun

Mathematics.

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

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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

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Etymology

Origin of continued fraction

First recorded in 1860–65

Example Sentences

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

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

There is, however, a different way in which a Series may be represented by a continued fraction.

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

The infinite general continued fraction of the first class cannot diverge for its value lies between that of its first two convergents.

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

The continued fraction is therefore incommensurable, and cannot be unity.

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