#### Document Type

Article

#### Publication Date

2004

#### 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*.

#### Publication Title

Proceedings of the American Mathematical Society

#### Volume

132

#### Issue

10

#### First Page

2973

#### Last Page

2981

#### Required Publisher's Statement

First published in "Proceedings of the American Mathematical Society" in 2004, published by the American Mathematical Society.

#### Recommended Citation

Ćurgus, Branko, "A Contraction of the Lucas Polygon" (2004). *Mathematics.* Paper 6.

http://cedar.wwu.edu/math_facpubs/6