publication . Article . 2014

The origins of Euler's early work on continued fractions

Cretney, Rosanna;
Open Access
  • Published: 01 May 2014 Journal: Historia Mathematica, volume 41, pages 139-156 (issn: 0315-0860, Copyright policy)
  • Publisher: Elsevier BV
Abstract
Abstract In this paper, I examine Euler's early work on the elementary properties of continued fractions in the 1730s, and investigate its possible links to previous writings on continued fractions by authors such as William Brouncker. By analysing the content of Euler's first paper on continued fractions, ‘De fractionibus continuis dissertatio’ (1737, published 1744) I conclude that, contrary to what one might expect, Euler's work on continued fractions initially arose not from earlier writings on continued fractions, but from a wish to solve the Riccati differential equation.
Subjects
free text keywords: History, General Mathematics, Algebra, Differential equation, Calculus, Mathematics, Riccati equation, Euler's formula, symbols.namesake, symbols, Bernoulli's principle
Communities
Digital Humanities and Cultural Heritage
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