Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A contraction of the Lucas polygon

Authors: Branko Curgus and Vania Mascioni
Journal: Proc. Amer. Math. Soc. 132 (2004), 2973-2981
MSC (2000): Primary 30C15; Secondary 26C10
Published electronically: May 20, 2004
MathSciNet review: 2063118
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $p$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30C15, 26C10

Retrieve articles in all journals with MSC (2000): 30C15, 26C10

Additional Information

Branko Curgus
Affiliation: Department of Mathematics, Western Washington University, Bellingham, Washington 98225

Vania Mascioni
Affiliation: Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306-0490

PII: S 0002-9939(04)07231-4
Keywords: Roots of polynomials, critical points of polynomials, Gauss-Lucas theorem
Received by editor(s): October 29, 2002
Received by editor(s) in revised form: February 12, 2003
Published electronically: May 20, 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia