Design of surfaces in cylindrical coordinates using GeoGebra AR - Flores-Osorio, Alejandro Isaías (2023)
This research focuses on the application of the definition of a convex set, which allows us to design and build the graph of bounded surfaces described by cylinders whose directrix curve is a polar curve that intersects with a quadric surface or a function defined in two variables and thus generates bounded surfaces to be constructed using the GeoGebra Suite Calculator. Three cases are presented where the importance of the convex set concept in the parameterization of this type of surface is highlighted. In the first case, we establish the surface that we have called the Flores surface and from this surface, we establish the construction of the Anthurium flower, in the second case we design the flower with 8 petals, and in the third case designed the leaf house modeled by Mareines and Patalano, whose structure is shaped like a flower with 6 petals. The construction of these surfaces is carried out using the GeoGebra Suite Calculator application for mobile devices, which through its GeoGebra AR tool allows these surfaces to be extended to an augmented reality environment and in this way visualize, manipulate, and understand the abstraction of these mathematical objects in a dynamic and interactive.