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

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

Any exact fraction can be expressed as a continued fraction, and there are methods for expressing as continued fractions certain other numbers, e.g. square roots, whose values cannot be expressed exactly as fractions.

From Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" by Various

“If in the infinite continued fraction of the second class an ≥ bn + 1 for all values of n, it converges to a finite limit not greater than unity.”

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

Conversely every positive quadratic surd number, when expressed as a simple continued fraction, will give rise to a recurring fraction.

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