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Continued fraction is a very useful tool of analysis. Many iterations-algorithms can be expressed easily using continued fraction. Continued fraction has nice property that it converge very fast (some are better than power series) and it can be useful to approximate the real number as ratio of two integers. This tutorial is an introduction to regular continued fraction (finite, infinite and periodic) and its application to convert decimal to fraction, compute Pi and Euler number. MS Excel spreadsheet companion of this tutorial can be downloaded for free

Contents:

What is Continued Fraction?

Why and when do we use Continued Fraction?

How do we compute Continued Fraction? (see: Continued Fraction Synthesis-Analysis Calculator)

Relationship of Continued Fraction and Difference Equation

Periodic Continued Fraction

Properties of Continued Fraction

Continued Fraction Using Mathematica

Applications

- Decimal to fraction conversion (see: Continued Fraction Calculator, code , online interactive program )
- Pi
- Euler Number
Resources on Continues Fraction

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See also
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:
Difference Equation tutorial

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This tutorial is copyrighted .

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Preferable reference for this tutorial is
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Teknomo, Kardi (2015) Continued Fraction. http://people.revoledu.com/kardi/tutorial/ContinuedFraction/index.html