A catenária no ensino médio: uma proposta de sequência didática

Abstract

The catenary curve is an intriguing mathematical and physical phenomenon that plays a crucial role in various fields, such as engineering, architecture, as well as being found in nature. Although the National Common Curricular Base (BNCC) states that Mathematics in high school should be integrated and applied to reality in various contexts, the catenary is not even mentioned as an example in textbooks. In this context, this work sought to address the question of how to explain this curve and its properties in high school. Therefore, the general objective is to investigate the mathematical properties and applications of the catenary curve and to propose a Didactic Sequence (SD) for high school. We present the relationship between the BNCC and the catenary, as well as its history, applications, and equation. Consequently, we developed the Educational Product (the SD) which includes a sequence of lessons for studying the catenary, with activities involving jump rope, soap bubbles, and constructing the catenary arch. It was concluded that studying the catenary in high school and using the SD can enhance the teaching and learning of Mathematics.