O uso de frações contínuas e do paradoxo de Galileu: aplicações na resolução de problemas físicos na educação básica

Abstract

In this paper, we describe the representation of a rational number in the form of continuous fraction sand later extend this representation to irrational numbers. We also enunciate Galileo's Paradox for infinite sets. Initially, with the aid of Euclidean division, we obtain the representation of a rational number in the form of continuous fractions and then through successive approximations, we obtain the representation of irrational numbers using these fractions. Then we articulate and exemplify the Galileo's Paradox for infinite sets. In addition, we use the continuous fractions and Galileo's Paradox to solve physical problems appropriate for k-12 education. Portilho and Lima [8] (2006, p. 26) suggest that such content rarely has been taught at this educational level, but in this text we seek to expose a proposal to be taught and exercised at this level. We conclude that these contents can be very useful in solving interesting problems of mathematics and Physics in k-12 education.