Search for a tool
Continued Fractions

Tool to compute continued fractions. A continued fraction is the representation of a number N in a form of a series of integers (a0, a1, ..., an) such as N = (a0+1/(a1+1/(a2+1/(...1/(an))).

Results

Continued Fractions -

Tag(s) : Series

Share
Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Feedback and suggestions are welcome so that dCode offers the best 'Continued Fractions' tool for free! Thank you!

Continued Fractions

Continued Fraction Calculator




Continued Fraction to Number Converter




Answers to Questions (FAQ)

How to calculate a continued fraction?

Continued fraction expansion is close to algorithm of euclidean division, as for PGCD.

Example: If the fraction approximating pi is $ 355/113 = 3.14159292035... $

$$ 355 = 3 \times 113 + 16 \\ 113 = 7 \times 16 + 1 \\ 16 = 16 \times 1 + 0 $$

The continued fraction is [3,7,16]

Some developments of continuous fractions are infinite

To find the corresponding fraction, use the irreducible fraction tool.

How to calculate the continued fraction of a root?

Calculate an approximate value of the root (approximation as accurate as possible) and dCode will provide the corresponding continuous fraction.

How to write a continued fraction in LaTex?

The easiest way is to use cfrac: $$ e=2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{ 1+\cfrac{1}{1+\cfrac{1}{4+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{6+\cdots}}}}}}}} $$

But the shortest way is to write $$ e = [2 ; 1, 2, 1, 1, 4, 1, 1, 6, \cdots] $$

Which are the most remarquable continued fractions?

Most known continued fractions are:

Square Root of 2: $ \sqrt{2} = [1;2,2,2,2,2,\cdots] $

— Golden Ratio: $ \Phi = [1;1,1,1,1,1,\cdots] $

Source code

dCode retains ownership of the "Continued Fractions" source code. Except explicit open source licence (indicated Creative Commons / free), the "Continued Fractions" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Continued Fractions" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Continued Fractions" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

Cite dCode

The copy-paste of the page "Continued Fractions" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Continued Fractions on dCode.fr [online website], retrieved on 2024-11-07, https://www.dcode.fr/continued-fractions

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Feedback and suggestions are welcome so that dCode offers the best 'Continued Fractions' tool for free! Thank you!


https://www.dcode.fr/continued-fractions
© 2024 dCode — El 'kit de herramientas' definitivo para resolver todos los juegos/acertijos/geocaching/CTF.
 
Feedback