Convexity in the Design of Bounded Surfaces and Unconventional Solids Using GeoGebra AR

Abstract

The present investigation focuses on the mathematical concept of convexity, as the main tool for the graphic construction of bounded surfaces explicitly and implicitly described, as well as the construction of unconventional solids using GeoGebra. Two cases are presented in which the importance of the concept of convexity is highlighted, in the first situation the convexity is used in the argument of the surface command together with the curves that delimit it to graph a bounded surface, while in the second situation the convexity is evidenced by expressing the coordinates of the surface in parametric form. On the other hand, the 3D graphic view combined with the GeoGebra AR tool allows one to visualize, manipulate, understand and improve the abstraction of mathematical objects that are built in three-dimensional space in a dynamic and friendly environment. These constructions in three-dimensional space that are complex when sketching them with pencil and paper are easier when linking the mathematical definitions with free software such as GeoGebra.