Integration of a CAS/DGS as a CAD system in the mathematics curriculum for architecture students

Abstract

Students of Architecture and Building Engineering Degrees work with Computer Aided Design systems daily in order to design and model architectonic constructions. Since this kind of software is based on the creation and transformation of geometrical objects, it seems to be a useful tool in Maths classes in order to capture the attention of the students. However, users of these systems cannot display the set of formulas and equations which constitute the basis of their studio. Moreover, if they want to represent curves or surfaces starting from its corresponding equations, they have to define specific macros which require the knowledge of some computer language or they have to create a table of points in order to convert a set of nodes into polylines, polysolids or splines. More specific concepts, like, for instance, those related to differential geometry, are not implemented in this kind of software, although they are taught in our Maths classes. In a very similar virtual environment, Computer Algebra and Dynamic Geometry Systems offer the possibility of implementing several concepts which can be found in the usual mathematics curriculum for Building Engineering: curves, surfaces and calculus. Specifically, the use of sliders related to the Euler's angles and the generation of tools which project 3D into 2D, facilitate the design and model of curves and rigid objects in space, by starting from their parametric equations. In this article, we show the experience carried out in an experimental and control group in the context of the Maths classes of the Building Engineering Degree of the University of Seville, where students have created their own building models by understanding and testing the usefulness of the mathematical concepts.