Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-01-10T14:58:57Z No. of bitstreams: 2 Dissertação - Pollyana Gomes Volpato - 2016.pdf: 1172027 bytes, checksum: 6e8ebfc67549380e690db90bc68b9104 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-01-11T09:42:09Z (GMT) No. of bitstreams: 2 Dissertação - Pollyana Gomes Volpato - 2016.pdf: 1172027 bytes, checksum: 6e8ebfc67549380e690db90bc68b9104 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-01-11T09:42:09Z (GMT). No. of bitstreams: 2 Dissertação - Pollyana Gomes Volpato - 2016.pdf: 1172027 bytes, checksum: 6e8ebfc67549380e690db90bc68b9104 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-12-09 / 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. / Temos como objetivo central neste trabalho demonstrar o Teorema de Marden, que nos diz que, dado um polinômio de terceiro grau com coeficientes complexos, as raízes desse polinômio não são colineares e formam um triângulo T no plano complexo. Há uma única elipse inscrita em T e tangente aos lados nos seus pontos médios. Os focos dessa elipse são as raízes da derivada do polinômio. Mostramos que tal elipse é a Elipse de Steiner. Fazemos uma generalização do Teorema de Marden utilizando polinômio de grau n.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-08T12:20:00Z No. of bitstreams: 2 Dissertação - Mario Jonas da Silva Santos - 2014.pdf: 1833814 bytes, checksum: 949d82c89c9bfa0c9361693ee94784ec (MD5) license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-08T12:46:39Z (GMT) No. of bitstreams: 2 Dissertação - Mario Jonas da Silva Santos - 2014.pdf: 1833814 bytes, checksum: 949d82c89c9bfa0c9361693ee94784ec (MD5) license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) / Made available in DSpace on 2015-10-08T12:46:40Z (GMT). No. of bitstreams: 2 Dissertação - Mario Jonas da Silva Santos - 2014.pdf: 1833814 bytes, checksum: 949d82c89c9bfa0c9361693ee94784ec (MD5) license_rdf: 21267 bytes, checksum: 73e23c2acaaf13389e092bd813e3223d (MD5) Previous issue date: 2014-09-26 / Let's start making an explanation of some important content. Starting with the set of complex numbers, polynomials, ellipse, derivative of a function in the complex variable and congruence triangles then we enunciate three lemma and demonstrates for them then enunciate and prove Theorem Marden. At the end we will have a proposal to class in the form of math workshop, students applied for the 3rd Series of high school. / Vamos começar fazendo uma explanação de alguns conteúdos importantes. Come çando com o conjunto dos números complexos, polinômios, elipse, derivada de uma função na variável complexa e conguência de triângulos em seguida vamos enuciar três lemas e demonstrá los para então enunciar e demonstrar o Teorema de Marden. Ao nal teremos uma proposta de aula em forma de o cina matemática, aplicada para alunos da 3a Série do ensino médio.