notation for continued fractions Cataldi represented a continued fraction as & & & 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 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. 1761 Johann Lambert – gave the first proof of the irrationality of using a continued fraction for 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 irrationals expand to periodic continued fractions. 1813 Carl Friedrich Gauss, Werke, Vol. 3, pp. 134–138 – derived a very general 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. See also Gaussian brackets Notes References External links Linas Vepstas Continued Fractions and Gaps (2004) reviews chaotic structures in continued fractions. Continued Fractions on the Stern-Brocot Tree at cut-the-knot The Antikythera Mechanism I: Gear ratios and continued fractions Continued fraction calculator, WIMS. Continued Fraction Arithmetic Gosper's first continued fractions paper, unpublished. Cached on the Internet Archive's Wayback Machine Continued Fractions by Stephen Wolfram and Continued Fraction Approximations of the Tangent Function by Michael Trott, Wolfram Demonstrations Project. A view into "fractional interpolation" of a continued fraction } Best rational approximation through continued fractions CONTINUED FRACTIONS by C. D. Olds Mathematical analysis