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Master's Dissertation
DOI
10.11606/D.55.2016.tde-31082016-110644
Document
Author
Full name
Claudio Xavier Mendes dos Santos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Mendes, Carlos Molina (President)
Santos, Leonardo Sioufi Fagundes dos
Vargas, Rosana Retsos Signorelli
Title in Portuguese
Circuitos resistivos autossimilares
Keywords in Portuguese
Circuitos autossimilares
Circuitos resistivos
Ensino da matemática
Fractais autossimilares
Funções iteradas
Grafos
Abstract in Portuguese
Esse trabalho é um estudo sobre circuitos resistivos que apresentam a característica da autossimilaridade em sua configuração. A construção desses circuitos é feita de uma maneira recursiva, de forma análoga a um fractal autossimilar. Os circuitos são analisados pelas suas resistências equivalentes, sendo obtida uma condição para convergência desse valor. Os conceitos auxiliares necessários ao tema desta dissertação abordam a representação de um circuito resistivo como um grafo, além de conceitos envolvendo fractais autossimilares. São propostas ao final de cada capítulo atividades interdisciplinares acessíveis a alunos de ensino médio, com conteúdos envolvendo resistência equivalente, sequências, conjuntos, e noções de área e perímetro.
Title in English
Autossimilar resistive circuits
Keywords in English
Autossimilar circuits
Graphs
Iterated functions
Math teaching
Resistive circuits
Self similar fractals
Abstract in English
This work is a study of resistive circuits which present a characteristic of self similarity in their configuration. The construction of these circuits is made in a self recursive way, analogously to a self similar fractal. The circuits are analyzed by their equivalent resistance, and a condition for convergence of this quantity is obtained. Auxiliary concepts that are necessary to this dissertation theme treat the resistive circuit as a graph, and concepts involving self similar fractals. It is proposed at the end of each chapter interdisciplinary activities that are accessible to high school students, with topics involving equivalent resistence, sequences, sets, and notions of area and perimeter.
 
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Publishing Date
2016-08-31
 
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