Short Stories

DOI10.1090/NOTI2384zbMATH Open1479.30003arXiv2112.00110OpenAlexW4200602853MaRDI QIDQ5029927

Publication date: 15 February 2022

Published in: Notices of the American Mathematical Society (Search for Journal in Brave)

Abstract: The Gauss-Lucas theorem says that for any complex polynomial

P

, the roots of the derivative

P^{'}

lie in the convex hull of the roots of

P

. In other words, the roots of

P^{'}

lie inside the smallest convex subset of the complex plane containing all the roots of

P

. This theorem is not hard to prove, but is there an intuitive explanation? In fact there is, using physics -- or more precisely, electrostatics in 2-dimensional space

Full work available at URL: https://arxiv.org/abs/2112.00110

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

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