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

A non-terminating simple continued fraction must be incommensurable.

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 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

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