Editing Simple continued fraction (section)

==History==
* 300 BCE ''[[Euclid's Elements]]'' contains an algorithm for the [[greatest common divisor]], whose [[Euclidean algorithm|modern version]] generates a continued fraction as the sequence of quotients of successive [[Euclidean division]]s that occur in it.
* 499 The ''[[Aryabhatiya]]'' contains the solution of indeterminate equations using continued fractions
* 1572 [[Rafael Bombelli]], ''L'Algebra Opera'' – method for the extraction of square roots which is related to continued fractions
* 1613 [[Pietro Cataldi]], ''Trattato del modo brevissimo di trovar la radice quadra delli numeri'' – first notation for continued fractions
:Cataldi represented a continued fraction as <math>a_0</math> & <math>\frac{n_1}{d_1 \cdot}</math> & <math>\frac{n_2}{d_2 \cdot}</math> & <math>\frac{n_3}{d_3 \cdot}</math> with the dots indicating where the following fractions went.
* 1695 [[John Wallis]], ''Opera Mathematica'' – introduction of the term "continued fraction"
* 1737 [[Leonhard Euler]], ''De fractionibus continuis dissertatio'' – Provided the first then-comprehensive account of the properties of continued fractions, and included the first proof that the number [[e (mathematical constant)|e]] is irrational.{{sfn|Sandifer|2006}}
* 1748 Euler, ''[[List of important publications in mathematics#Introductio in analysin infinitorum|Introductio in analysin infinitorum]]''. Vol. I, Chapter 18 – proved the equivalence of a certain form of continued fraction and a generalized [[infinite series]], proved that every rational number can be written as a finite continued fraction, and proved that the continued fraction of an irrational number is infinite.{{sfn|Euler|1748}}
* 1761 [[Johann Lambert]] – gave the first proof of the irrationality of [[Pi|{{pi}}]] using a continued fraction for [[Trigonometric functions|tan(x)]].
* 1768 [[Joseph-Louis Lagrange]] – provided the general solution to Pell's equation using continued fractions similar to Bombelli's
* 1770 Lagrange – proved that [[quadratic irrational number|quadratic irrationals]] expand to [[periodic continued fraction]]s.
* 1813 [[Carl Friedrich Gauss]], ''Werke'', Vol. 3, pp.&nbsp;134–138 – derived a very general [[Gauss's continued fraction|complex-valued continued fraction]] via a clever identity involving the [[hypergeometric function]]
* 1892 [[Henri Padé]] defined [[Padé approximant]]
* 1972 [[Bill Gosper]] – First exact algorithms for continued fraction arithmetic.