A geometria do conjunto de Cantor, do tapete de Sierpinski e da esponja de Menger

Abstract

This work is inserted in the context of the Professional Master’s Program in Mathematics in National Network - PROFMAT and presents the construction of the Cantor set. To display the properties of the Cantor set, we explored contents present in the National Curriculum of Basic Education in Mathematics, such as sets, functions, real intervals and geometric progressions. We use language accessible to elementary school students and present activities involving other fractals, obtained in a similar way to the Cantor set, as well as the Sierpinski rug and the Menger sponge.