Drawing and Mathematics. An Integrated Teaching

  • Alberto Lastra SedanoEmail author
  • Manuel de Miguel Sánchez
  • Enrique Castaño Perea
  • Ernesto Echeverría Valiente
Conference paper


In 2011 it was started, at the School of Architecture of Alcalá, a new course called: Taller de Dibujo II. Its main goal was to convey the importance of studying an architectural object from different points of view. The link would be the geometry, the coordinated subjects: design and mathematics. Teachers from both departments began an integrating task. They had two different ways of understanding teaching. It would be a subject in constant evolution. So we started an educational innovation project, which is ongoing (UAH/EV519). In the last ten years the importance of the parameterization has grown significantly in fields like design, engineering and architecture. Our School of architecture implemented an interdisciplinary group that was able to introduce these new skills. “The rigorous parameterization requires the assimilation of concepts much closer to mathematic geometry and software programming” (Coloma and Mesa in Revista EGA 19:200, 2012). But some experiences around the subject have put their emphasis on tools, neglecting, in our opinion, the methodological basis. Although traditional teaching materials are not fully useful to this new subject, accumulated experiences are very valuable. Grassa-Miranda and Giménez (Revista EGA 15:156, 2010) regarding the traditional teaching of geometry states that “The grammar or guiding principles of the Spanish sistema diédrico uses the projective schema of a model to build the student’s spatial thinking, while the Anglo-Saxon direct method relies on the reconstruction of a mental image of the geometric configuration” In a similar way, we considered the importance of the object opposite to the system, or the process. Therefore, the starting points of our methodology are the works of architecture and engineering. Objects with a complex geometry, especially those which curves and surfaces are able to be parameterized. The curve and surface become that way, protagonists of the experience. The next step is to thoroughly analyze through operations of modification and intersection. A good analysis of a work with a complex geometry, involves the preliminary study of the project and the knowledge of the difficulties and intentions of the author. Often the most interesting geometric designs arise from the need of finding creative solutions for complex problems with the most simple and balance response, as a whole. Many of the works built by Torroja, Candela, Dieste, Maillart, Isler, Freyssinet, Frei Otto, Fisac and many others, show that the study of the object cannot be limited to the representation of form. In this article we will show our experience and several possibilities to develop about the subject. We will describe the overall strategy and present some concrete exercises defining our scope. Finally we will propose several alternatives for further applications in future editions of the course.


Teaching of geometry Architectural geometry 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Alberto Lastra Sedano
    • 1
    Email author
  • Manuel de Miguel Sánchez
    • 2
  • Enrique Castaño Perea
    • 2
  • Ernesto Echeverría Valiente
    • 2
  1. 1.Department of Physics and MathematicsUniversidad de AlcaláAlcalá de HenaresSpain
  2. 2.Department of ArchitectureUniversidad de AlcaláAlcalá de HenaresSpain

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