Estudo da fração contínua e suas aplicações

Abstract

This dissertation aims to present the Theory of Continuous Fractions as a strategic model to create approximations of the sets of Rational and Irrational numbers, exposing the context and its advances relative to the possibilities of commensurable and incommensurable segments, using the converging finite and infinite continuous fractions for the understanding and meaning of the Theory as well as showing the importance of good approximation and use of the model in different areas of knowledge. The theme exists in the curriculum of teaching however, there remains a great difficulty to present the sets of rational numbers for the Real, but also because the Fractions Continuous model to deal with the level of complexity that the subject presents. Therefore, I suggest that this subject be treated and debated in Basic Education, but not as a curricular theme, but as an instrument for application in various contents already foreseen in the final years of Elementary and Middle School. The production of the theoretical reference was made from articles, dissertations, theses, books and websites referring to the research work.