Editing Simple continued fraction (section)

===Periodic continued fractions===
{{main|Periodic continued fraction}}
The numbers with periodic continued fraction expansion are precisely the [[quadratic irrational|irrational solutions]] of [[quadratic equation]]s with rational coefficients; rational solutions have finite continued fraction expansions as previously stated. The simplest examples are the [[golden ratio]] φ = [1;1,1,1,1,1,...] and {{sqrt|2}} = [1;2,2,2,2,...], while {{sqrt|14}} = [3;1,2,1,6,1,2,1,6...] and {{sqrt|42}} = [6;2,12,2,12,2,12...]. All irrational square roots of integers have a special form for the period; a symmetrical string, like the empty string (for {{sqrt|2}}) or 1,2,1 (for {{sqrt|14}}), followed by the double of the leading integer.