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

Converting a b into a continued fraction and proceeding as before, we obtain, in the case of aq − bp = 1, x = cq − bt, y = at − cp.

From Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 "Equation" to "Ethics" by Various

If a or b is unity, a/b cannot be converted into a continued fraction with unit numerators, and the above method fails.

From Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 "Equation" to "Ethics" by Various

For the convergence of the continued fraction of the second class there is no complete criterion.

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

A continued fraction may always be found whose nth convergent shall be equal to the sum to n terms of a given series or the product to n factors of a given continued product.

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