A visualização da natureza através da geometria fractal: explorando a beleza infinita na educação matemática

Abstract

This study aims to provide high school teachers with alternative methods that enable dynamic classroom instruction, based on Fractal Geometry with an emphasis on the visualization of nature’s resources. To this end, the research is classified as qualitative, exploratory in nature, and employs bibliographic procedures, reviewing 27 works by 26 authors, dated from 1982 to 2025. Among these are Freire Rabay (2013), Mandelbrot (1982), and Barbosa (2005), among others, with the purpose of demonstrating that the teaching of Fractal Geometry is relevant to arousing students' curiosity and interest in Science and the world in which they live. A didactic proposal is presented as a product of the research. Through this investigation, it was found that an efficient approach to teaching Fractal Geometry can be achieved through a review of the specialized literature—exploring the contributions of major theorists—and by observing nature to identify and systematize seemingly chaotic geometric patterns. Moreover, the study suggests that future research expand the scope to include elementary school students and deepen the bibliographic review in disciplines such as the History of Mathematics, in addition to promoting teacher training courses for educators who lack the repertoire to work with this approach.