História da Matemática e Animações com Manim: Estratégias Visuais para o Ensino de Cálculo Integral

Abstract

This paper presents the results of a qualitative research study with a bibliographic approach, whose objective was to investigate the potential of using animations produced with Manim software in teaching the concept of area in integral calculus. It is a historical-didactic analysis that combines knowledge of the history of mathematics with digital technologies, seeking to facilitate the understanding of abstract content through visual and interactive resources. Based on the analysis of historical episodes fundamental to the development of the concept of area, such as the methods of Eudoxus, Archimedes, Al-Khwārizmī, Cavalieri, Newton, Leibniz, and Riemann, four animations were created with Manim, highlighting key moments in this conceptual trajectory. Analysis of these materials indicated that well-structured visual representations facilitate the understanding of complex mathematical ideas, connecting the past of mathematics to the current languages of students. Although the use of Manim requires basic programming knowledge, the results highlight its educational potential, especially in the initial training of teachers. It is concluded that the integration of the history of mathematics and technology is a promising strategy for making teaching more meaningful, creative, and accessible, in addition to promoting pedagogical practices aligned with Science, Technology, Engineering, Arts, and Mathematics (STEAM) education.