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 continued fraction, of the kind we are considering, is an expression of the form where b, c, d, ... are integers, and a is an integer or zero.

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

The theory and development of the simple recurring continued fraction is due to Lagrange.

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

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

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