Geometria de fractais : caracterização matemática dos sistemas naturais no ensino da educação básica

Abstract

Fractal Geometry is an area of mathematics that studies complex geometric shapes, characterized by their self-similarity, infinite complexity, roughness, and fractal dimension. The application of this geometry in environmental systems allows the identification of patterns and complex structures, which can be used in the understanding and analysis of natural phenomena, such as the distribution of plants in a forest, lightning formation, cloud formation, formation of the terrestrial coast or the shape of a river. The present dissertation has the general objective of elaborating and testing a didactic sequence that applies Fractal Geometry in environmental systems, aiming to facilitate the learning of mathematical and physical concepts in search of the development of logical thinking in the characterization of environmental systems for use in teaching situations and learning. The use of the didactic sequence method, using the three pedagogical moments of the authors Delizoicov, Angotti and Pernambuco applied to Fractal Geometry in environmental systems, proves to be an efficient strategy to achieve this objective. For the development of this research, the qualitative method of investigation was used, according to Bogdan, Biklen and Bardin. This method allows a detailed and systematic analysis of the collected data, to identify patterns and trends in relation to the use of Fractal Geometry in environmental systems. Considering the results obtained in the research, the application of fractal geometry as a pedagogical tool and its use in several fields of knowledge, such as medicine, topology, engineering, among others. Furthermore, it emphasizes the application of this approach in studies of environmental systems, such as forests, rivers, and watersheds, which are characterized by their complexity and heterogeneity. Fractal geometry allows analyzing and describing the complexity of these systems more accurately and efficiently, enabling the identification of fractal patterns in the structure and dynamics of these systems. The application of this approach can contribute to the understanding of the ecological and hydrological processes that occur in these systems and to the orientation of public policies and practices of environmental conservation, promoting the sustainability and preservation of natural resources. At the end of this study, it is expected to make elements available for use in other educational contexts, contributing to the expansion of knowledge and to the formation of students with greater analytical and critical capacity.