# `quadratic-irrational`
[](https://travis-ci.org/ion1/quadratic-irrational)
A library for exact computation with [quadratic irrationals][qi] with support
for exact conversion from and to [(potentially periodic) simple continued
fractions][pcf].
[qi]: http://en.wikipedia.org/wiki/Quadratic_irrational
[pcf]: http://en.wikipedia.org/wiki/Periodic_continued_fraction
A quadratic irrational is a number that can be expressed in the form
```
(a + b √c) / d
```
where `a`, `b` and `d` are integers and `c` is a square-free natural number.
Some examples of such numbers are
* `7/2`,
* `√2`,
* `(1 + √5)/2` ([the golden ratio][gr]),
* solutions to quadratic equations with rational constants – the [quadratic
formula][qf] has a familiar shape.
[gr]: http://en.wikipedia.org/wiki/Golden_ratio
[qf]: http://en.wikipedia.org/wiki/Quadratic_formula
A simple continued fraction is a number in the form
```
a + 1/(b + 1/(c + 1/(d + 1/(e + …))))
```
or alternatively written as
```
[a; b, c, d, e, …]
```
where `a` is an integer and `b`, `c`, `d`, `e`, … are positive integers.
Every finite SCF represents a rational number and every infinite, periodic SCF
represents a quadratic irrational.
```
3.5 = [3; 2]
(1+√5)/2 = [1; 1, 1, 1, …]
√2 = [1; 2, 2, 2, …]
```