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GEOMETRY IN MOTION. BETWEEN RESEARCH, EDUCATION AND OUTREACH

S. Benvenuti, I. Giancamilli, A. Renieri

Università di Camerino (ITALY)
In every type of dance there are many mathematical concepts used (sometimes) unconsciously both to find harmony of human bodies in the space, and for the logic.

In our talk we will explore the connections between mathematics and dance, understood as a movement of the body itself. The idea is to use the human body and the space that surrounds it in order to introduce important concepts of Geometry and, in general, Mathematics.
Our main two experimentation are a dance show called “Intrecci”, composed of four main choreographies, and a series of laboratories dedicated to different kind of students (from Preschool to University).

First of all we will show a short video of Intrecci. This show was designed and implemented by ourselves together with the students of the dance school MiLaDance of Serra de' Conti (Ancona, Italy). In the show, using the modern dance, we introduce and clarify the isometries of the space and the concept of homothety. Moreover, we work on the music, which not only acts as an accompaniment, but is an integral part of the show.

Then we present some different application on different kind of school (preschool, primary, etc.). In those activities we have kept in mind that the excellent learn path consists of the triad “do-see-symbolize” and that, as Emma Castelnuovo said, we can do “les mathématiques avec les mans sales!”.

After this brief introduction, the central part of the talk will be dedicated to a practical example of what we mean by "doing geometry with the body." More precisely, we will play with the bodies (and the heads) of the participants on the concepts of translation, reflection, rotation and glide reflection, and we will construct together, jumping and dancing, all the seven possible kinds of frize.