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

DOI:
https://doi.org/10.1090/S0002-9939-04-07231-4

Published electronically:
May 20, 2004

MathSciNet review:
2063118

Full-text PDF

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 lie in the convex hull of the roots of , called the Lucas polygon of . We improve the Gauss-Lucas theorem by proving that all the nontrivial roots of lie in a smaller convex polygon which is obtained by a strict contraction of the Lucas polygon of .

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Additional Information

**Branko Curgus**

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

DOI:
https://doi.org/10.1090/S0002-9939-04-07231-4

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