Das películas de sabão às superfícies mínimas

Abstract

This work presents an initial study of curves in the three-dimensional space and the regular parameterized surfaces to approach finally the geometric properties of the minimal surfaces. These surfaces are generally associated with soap films, due to experiments using closed contours by immersed wires in a mixture of water and soap accomplished by Plateau. The problem would be, without great rigor, obtaining a surface of minimal area which has a determined closed contour in the space as border. From the studies carried out involving the fascinating minimal surfaces, it will be suggested at the end of the work that these surfaces be addressed in an introductory way in high school math classes, through the use of pedagogical strategies that interact with the student’s concrete reality from a contextualized approach that allows the student to observe, interpret and build knowledge in this very charming “universe” which is the universe of minimal surfaces.