Examples for

Continued Fractions
The continued fraction representation of a number is a sum of two terms. The first is the number's integer part. The second is recursively defined as the reciprocal of the continued fraction form of the reciprocal of the original number's fractional part. Rational numbers can be represented by finite continued fractions while irrationals require infinitely deep representations. Wolfram|Alpha can be used to convert between and utilize these representations. It also possesses knowledge about symbolic continued fractions as well as related theorems and algorithms.

Numbers

Convert between decimal and continued fraction representations of numbers.

Find the continued fraction representation of a number:

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Functions

Convert between regular and continued fraction representations of functions.

Find continued fraction representations for a function:

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Definitions of Terms

Learn about the meanings of terms and phrases relevant to the area of continued fractions.

Find definitions for continued fraction terminology:

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Theorems

Learn about theorems related to continued fractions. Apply them and see where and how they are applied.

Get information about a continued fraction theorem:

Find theorems that apply to a specified expression:

Find theorems by application:

Find theorems by prover:

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Algorithms

Learn about and use different algorithms for finding and working with continued fraction representations.

Get information about a continued fraction algorithm:

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Literature

Search for literature relevant to the area of continued fractions.

Find continued fraction papers by author:

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Interactive Visualizations

Use visual tools to aid your intuition in the area of continued fractions.

Explore continued fraction results with interactive visualizations:

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