2024/01/22 by Andrey Ryabichev, Ryabichev, Andrey, Konstantin Shcherbakov +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2401.12394
openalex publication_date 2024/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a real cubic function f(x) with three roots, take an equilateral triangle ABC, the projections of which vertices are the roots of f(x). There is a folklore fact that the vertical lines through the extrema of f(x) are tangent to the inscribed circle of ABC. We generalise this fact to a regular n-gon and the corresponding degree n polynomial.