Geometria Fractal: uma abordagem com aplicações voltada ao 3° ano do ensino médio

Abstract

This work was elaborated with the objective of making an elementary approach of fractal geometry to students of the 3rd Year of High School, showing some classic characteristics and some aspects related to the theory of fractals. Initially, a brief approach is made to Euclidean geometry and some characteristics of other geometries. Next, the study of fractal geometry begins, emphasizing that it allows observing an interesting connection between the construction of mathematical elements and some objects present in nature. Some classic fractals were presented, such as the Koch curve, the Cantor set, the triangle and the Sierpinski carpet. The mathematical characteristics of these objects were discussed with the participants of this research, especially their size, which reflects a peculiar characteristic of fractals and which differs them in relation to objects of Euclidean geometry. The results indicated that the approach of fractal geometry with high school students contributes to their motivation and interest in the study of mathematics, in addition to expanding their understanding of geometric concepts.