A Contraction of the Lucas PolygonProceedings of the American Mathematical Society
AbstractThe 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 InformationBranko 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/