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))).
Continued Fractions - dCode
Tag(s) : Series
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!
Continued Fractions
Sponsored ads
Continued Fraction Calculator
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))).
Answers to Questions
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 simple fraction, use the irreducible fraction tool.
How to calculate the continued fraction of a root?
Calculate an approximate value of the root (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 source code of the script Continued Fractions online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Continued Fractions script for offline use on PC, iPhone or Android, ask for price quote on contact page !
Questions / Comments
Lire en Français
or 
