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 withComputer Aided Design systems daily in order to design and modelarchitectonic constructions. Since this kind of software is based on thecreation and transformation of geometrical objects, it seems to be a usefultool in Maths classes in order to capture the attention of the students.However, users of these systems cannot display the set of formulas andequations which constitute the basis of their studio. Moreover, if they wantto represent curves or surfaces starting from its corresponding equations,they have to define specific macros which require the knowledge of somecomputer language or they have to create a table of points in order toconvert a set of nodes into polylines, polysolids or splines. More specificconcepts, like, for instance, those related to differential geometry, are notimplemented in this kind of software, although they are taught in ourMaths classes. In a very similar virtual environment, Computer Algebraand Dynamic Geometry Systems offer the possibility of implementingseveral concepts which can be found in the usual mathematics curriculumfor Building Engineering: curves, surfaces and calculus. Specifically, the useof sliders related to the Euler’s angles and the generation of tools whichproject 3D into 2D, facilitate the design and model of curves and rigidobjects in space, by starting from their parametric equations. In this article,we show the experience carried out in an experimental and control group inthe context of the Maths classes of the Building Engineering Degree of theUniversity of Seville, where students have created their own buildingmodels by understanding and testing the usefulness of the mathematicalconcepts.