Algoritmos de aproximação de raízes quadradas

• Autor(a) principal: CAMPOS, Danilo Albuquerque de
• Data de Publicação: 2014
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFRPE
• Texto Completo: http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6699
• topic: Theorem of Dirichlet; Square root; Equação de Pell-Fermat; Escada de Theon; Algoritmos de Hierão; Teorema de Dirichlet; Aproximação racional; Raiz quadrada; Rational approximation; Algorithms Hiero; Ladder Theon; Pell-Fermat equation; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work we are interested in showing three algorithms rational approximation of square roots by methods unknown or underutilized by teachers of elementary and secondary education. We begin by defining numerical sequence and convergence of sequences, will discuss the need to expand the concept of rational number and demonstrate the irrationality of the diagonal of a square. Prove an important theorem known in the literature as Dirichlet’s theorem and finally elencaremos three methods of approximating the square roots of natural non-perfect square numbers, very simple to be worked on in the classroom that are rational algorithm aproximção of Hiero of Alexandria, Theon’s Ladder and the Pell-Fermat equation, sende latter discursão fundamental to who will perform on the relationship of the three methods presented.