O equilíbrio dos planos e os pontos notáveis do triângulo: Arquimedes, Euclides e origami trabalhando juntos

Abstract

This paper aims to explore a new way to study geometry during the High School, using physics and origami. We use classical works of Archimedes and Euclid to rise the mathemathical way to study the properties of the plane figures’ center of mass and the triangle’s notable points. Walking on the knowledge timeline we add some contributions made by the french mathematician Hadamard and modern ways to teaching geometry at school. In fact, we try to compare old and modern classroom practices. Them, we present some aspects about the origin of origami in Japan and paperfolding in western contries. After, we talk about Huzita-Hatori Axioms in mathematical terms. In order to use the natural young people curiosity about things we show the physical center of mass concept and argue about the geometry usefulness in the real world. Finally, we present how its possible to work in two diferente ways to find the plane figures’ center of mass and the triangle’s notable points: the classical way, using a straight edge and a compass for the mathematical constructions and the funny way, using origami to do the same. All of these will be done looking foward teachers and students realize that’s possible to have good time while they are studing Mathematics. We also hope this work may inspire teachers to encourage their students to share mathematical knowlegmente outside the school.