Los workshops de geometría en Cad3d y prefabricación digital como estrategia docente en la enseñanza de la geometría para la arquitectura. geometría y proyecto Workshops about geometry, 3dCad and digital fabrication as a teaching strategy for architectural geometry learning. geometry and design studio This paper shows the approaches and results of an innovation teaching project carried out in the University of Seville and the National University of Colombia. The purpose is to teach architectural geometry within collaborative teams of professors and groups of 25 students. Through a guided exercise, students work on the relationship between geometry and all the phases of the typical architectural process, applying geometry to solve real problems. It begins with the ideation, digital construction and resolution of construction, to conclude with the physical execution of the project.
A graphic conjecture is presented based on a singular property stated by in his work On Conoids and Spheroids. This ancient text constitutes the starting argument for graphic research that has revealed an unknown property regarding the intersection of rotational quadratic surfaces which they share one of their foci. This article shows the heuristicgeometric reasoning carried out stemming from Archimedes' text transcriptions and a conjecture that can be deduced when the initial property is generalised for the rest of the quadratic surfaces. Moreover, an explanation is offered for the possibilities of this property to be used for the discretisation of architectural surfaces through the use of parametric design and digital fabrication.The property discovered in this research is summarised as follows: "If two rotational quadratic surfaces share the position of one of their foci at the same point, then the intersection curves between the two surfaces are always planar". 1 This new property, which currently remains only a conjecture 2 , has been formulated from purely graphic thinking. However, its validity has been fully tested through a heuristic method which involves checking the planarity on all possible combinations of quadric intersections in a necessary and sufficient number of cases. For this purpose, the power of CAD tools has been used as a true geometric research laboratory where the validity of the theoretical approaches is subject to trial and error.
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