O teorema de Marden e uma generalização

• Autor(a) principal: Volpato, Pollyana Gomes
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000002j8g
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6705
• topic: Elipse de Steiner; Teorema de Marden; Generalização do teorema de Marden; Polinômios com coeficientes complexos; Steiner’s ellipse; Marden’s theorem; Generalization of Marden’s theorem; Polynomials with complex coefficients; CIENCIAS EXATAS E DA TERRA::MATEMATICA

The main objective of this work is to demonstrate Marden’s Theorem, which tells us that given a third-degree polynomial with complex coefficients, the roots of this polynomial are not collinear and form a triangle T in the complex plane. There is a unique ellipse inscribed in T and tangent to the sides at their midpoints. The foci of this ellipse are the roots of the derivative of the polynomial. We show that such an ellipse is Steiner’s Ellipse. We make a generalization of the Marden Theorem using degree n polynomial.