Frações e a geometria: algumas conexões entre as sequências de Farey, os círculos de Ford e os Sangakus

Abstract

This work is a bibliographic study based on books, articles and theses. It aims to create a didactic sequence in order to offer students and teachers of Primary Education a new perspective on the content of fractions and plane geometry. In this study, these contents are related to each other and new concepts are presented that use these relationships, such as the Farey sequences, the Ford circles and the Sangakus. For its realization, the Brazilian legislation was used as a theoretical reference, such as the National Curriculum Parameters and the Common National Curriculum Base and studies present in the literature that deal with the Farey sequences, the Ford circles and the Sangakus. The research followed the following steps: identification of the contents and the way that they would be approached in a task, creation of the task and creation of a questionnaire to determine the opinions and evaluations of the students. This task was built to be worked with students of Primary Education, from the 9th year of Elementary School and, it is hoped, with its development to arouse interest in students in the discipline of mathematics and in its history.