Aplicações das superfícies mínimas na arquitetura: teoria e uma proposta para o ensino médio

Abstract

In this work, the minimal surfaces are studied and presented in a way that arouses curiosity about the theme so that it can be reached by mathematicians, architects, students and people who are interested in the subject. We will introduce the historical context in order to arouse the reader's curiosity for the theory, ranging from the experiments with soap films and their applications, to the mathematical concepts that involve the minimal surfaces. The countless applications of these surfaces are accompanied by a natural beauty that pleases and arouses the interest of any observer. The challenge, which has intrigued mathematicians for centuries, of finding the surface of the smallest area given a fixed outline, nature solves and shows ways to apply it in our homes and living spaces in general. In this sense, the theory is followed by applications with an emphasis on architecture and its main exponents. Finally, the results of our own experiments with soap films will be presented, as well as suggestions for activities to be done with high school students that motivate the study of our theme.