Continued fraction Totally Explained

Everything about Continued Fractions totally explained

In mathematics, a continued fraction is an expression such as ť

x = a_0 + cfrac

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 is irrational.

1748 Leonhard Euler, 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.

1768 Joseph Louis Lagrange - provided the general solution to Pell's equation using continued fractions similar to Bombelli's

1770 Joseph Louis Lagrange - proved that quadratic irrationals have a periodic continued fraction expansion

1813 Karl Friedrich Gauss, Werke, Vol. 3, pp. 134-138 - derived a very general complex-valued continued fraction viā a clever identity involving the hypergeometric series

1972 Bill Gosper. - First exact algorithms for continued fraction arithmetic.Further Information

Get more info on 'Continued Fractions'.

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