Chebyshev e a variação de um polinômio

Abstract

The present work addresses a problem proposed in 1854 by the Russian mathematician Pafnuty Chebyshev, regarding the Minor Variation of a Polynomial.This work aims to solve, by geometric means, the problem proposed by Chebyshev. To make this possible, we divided it into 3 chapters: We will present in the 1st chapter some important definitions and theorems in mathematics, which will facilitate the understanding of the resolution, as well as provide us with an appropriate theoretical basis for this purpose. In the 2nd chapter we will start by conceptualizing the Variation of a Polynomial and a specific notation for it, aiming at an easy understanding of what will be exposed. Soon after, the solution of the problem of Chebyshev itself, aided by graphical representations of the polynomials involved and more other theorems. Chapter 3 aims to define trigonometrically the Chebyshev polynomials of types Tn and Un, to present the calculation of the first polynomials and their respective graphical representations, their recurrence relations.