2006/07/01 by R. W. D. Nickalls · 79 citations
Mathematics · Social Sciences · #Algebraic number #Computer science #Cubic function #Geometry #Historical and Literary Studies #History and Theory of Mathematics #Mathematical analysis #Mathematics #Mathematics and Applications #Theme (computing)
paper · doi:10.1017/s0025557200179598
published in The Mathematical Gazette 90(518), 203-208 (Cambridge University Press)
openalex publication_date 2006/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/19
An appreciation of the geometry underlying algebraic techniques invariably enhances understanding, and this is particularly true with regard to polynomials.With visualisation as our theme, this article considers the cubic equation and describes how the French mathematicians François Viète (1540–1603) and René Descartes (1596–1650) related the ‘three-real-roots’ case (casus irreducibilis) to circle geometry. In particular, attention is focused on a previously undescribed aspect, namely, how the lengths of the chords constructed by Viète and Descartes in this setting relate geometrically to the curve of the cubic itself.