Rhythm, a motivation to study geometry

Abstract

One of the main concerns of Mathematics teachers in Technical Schools of Engineering and Architecture is how to draw our students’ attention and interest for the subject we teach. We have widely discussed this general worry in many occasions. The Research Group MAIC (Mathematics Applied to Civil Engineering) establishes among their aims to foster active participation among students in the process of learning - teaching Mathematics. The “Workshops to approach Mathematics” play a relevant role to achieve this aim. This new learning model is based on practical activities with students. This paper reports on one of them, a Workshop to introduce first year students in the study of proportions through a presentation of masterpieces of painting, architecture and art. The theoretical foundations of this methodology are several definitions of proportion. Vitrubio, (I a. C) defines proportion as the commensurability of each of the members in a work and of all the members in the whole by a specific measure unit or module (De architectura, book I). In his Teoria dell’ architettura, Bruno Taut ensures that the only aspect that acts in architecture is the sense of proportions. The essential aim of the theory of proportion is visual intentionality, which consists in creating an apparent order by the repetition of similar figures and their form intentionality, based, not on the forms themselves but on the rhythm among such forms. The similarity of figures in geometry and the analogy of planes and volumes in architecture emerge from this rhythm. The activities carried out in the Workshops can be further developed with computer tools and software to obtain designs corresponding to the studied proportions. This teaching experience will be presented from a multidisciplinary perspective by using an artistic approach to both architecture and civil engineering works. Among other aspects, the results show that, if study topics are in a direct relationship with the students’ interest centers, motivation increases.