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Article
A Contraction of the Lucas Polygon
Proceedings of the American Mathematical Society
  • Branko Ćurgus, Western Washington University
Document Type
Article
Publication Date
1-1-2004
Disciplines
Abstract

The celebrated Gauss-Lucas theorem states that all the roots of the derivative of a complex non-constant polynomial p lie in the convex hull of the roots of p, called the Lucas polygon of p. We improve the Gauss-Lucas theorem by proving that all the nontrivial roots of p' lie in a smaller convex polygon which is obtained by a strict contraction of the Lucas polygon of p.

Citation Information
Branko Ćurgus. "A Contraction of the Lucas Polygon" Proceedings of the American Mathematical Society Vol. 132 Iss. 10 (2004) p. 2973 - 2981
Available at: http://works.bepress.com/branko_curgus/4/