A contraction of the Lucas polygon
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- by Branko Ćurgus and Vania Mascioni PDF
- Proc. Amer. Math. Soc. 132 (2004), 2973-2981 Request permission
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
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Additional Information
- Branko Ćurgus
- Affiliation: Department of Mathematics, Western Washington University, Bellingham, Washington 98225
- Email: curgus@cc.wwu.edu
- Vania Mascioni
- Affiliation: Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306-0490
- Email: vdm@bsu-cs.bsu.edu
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2973-2981
- MSC (2000): Primary 30C15; Secondary 26C10
- DOI: https://doi.org/10.1090/S0002-9939-04-07231-4
- MathSciNet review: 2063118