Abstract:

The project 3D Explora, supported by the Universidad Politécnica de Madrid, originated in 2018 in the interests and concerns of the professors participating in the Innovative Educational Group MAMI (MAMI is a Spanish acronym from of “Improvement of Mathematical Learning in Engineering Education”). The main goal of this educational research project is to provide an online didactic resource for the visualization of curves and surfaces in three-dimensional space, aimed at facilitating the understanding of abstract and applied geometrical notions, especially with respect to objects that vary dynamically in terms of some parameters. The resource is intended for students and professors of engineering and architecture in which geometric intuition is much needed. Although there exist many computational resources for visualizing curves and surfaces in 3D, in particular CAD (Computer Aided Design) software, generally this software is not focused on developing abstract geometric understanding. On the other hand, in many cases a good understanding of the mathematical properties of geometric objects helps in making better use of this sort of software, so common in professional work. There are also available three-dimensional interactive visualization resources linked to formal mathematical descriptions but they often lack the accompanying explanations and references needed to understand them fully. In this context, the project 3D Explora aims to supply a self-explanatory online visualization resource. The resource consists of a Geogebra book of interactive and dynamic geometric constructions accompanied by mathematical descriptions and short explanations suitable for blended learning. Geogebra is an open source platform for noncommercial purposes that has a large community of users sharing apps and designs. It provides tools for linear algebra, geometry, statistics, and calculus. The 3D Explora digital library is already being successfully employed in several math courses taught in degree programs of the Universidad Politécnica de Madrid and other universities linked to teachers participating in this educational research project.

Keywords:

3D visualization, curves and surfaces, digital library, educational research project.