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# xinxinw1 / cont-frac Public

Continued Fractions

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# Continued Fractions

Run it at https://xin-xin.me/code/cont-frac/

This program makes it easy to study continued fractions.

## Usage

There are 4 sections: (frac | dec | func | cont)

Take note that if you switch sections, your data in the previous section will be lost!

### frac

This converts a normal fraction into a continued fraction. Input the numerator and denominator as two integers. (ex. 1578275893 / 2987598372947)

If you type a `/` in the first box, it automatically switches to the second box.

In all sections, `nprec` is the number of decimal places for the decimal number output.

### dec

This converts a decimal number into a continued fraction. Input a number like `2.718281828459045235360287471353`

### func

This uses two Javascript functions to generate the partial numerators and partial denominators of a generalized continued fraction. In this program, `a(n)` are the numerators and `b(n)` are the denominators so that the final number is

``````a(0) + b(1) / (a(1) + b(2) / (a(2) + ...))
``````

To run the program, click inside the nprec box, and press Enter or change the number.

For example, this gives the golden ratio

a(n)

``````return 1;
``````

b(n)

``````return 1;
``````

This gives Euler's number e:

a(n)

``````if (n == 0)return 2;
if (n % 3 == 1)return 1;
if (n % 3 == 2)return ((n+1)/3)*2;
if (n % 3 == 0)return 1;
``````

b(n)

``````return 1;
``````

### cont

This converts a continued fraction into a regular fraction and a decimal number.

It takes continued fraction in a form like this:

``````[0; 1, 2, 3, 4, 5, 6, 7, 8, 9]
``````

Whitespace and square brackets are optional. Either `;` or `,` can be used as delimiters.

That means that this works just as well:

``````0,   1,2, 3 ,4 , 5, 6,7 ,8,9  ]
``````

This program is dedicated to the public domain using the Creative Commons CC0. See `LICENSE.txt` for details.

Continued Fractions