We are a team of mathematicians and architects of Politecnico di Torino (Italy); in addition to our research subjects we are interested to new interdisciplinary teaching methods. One of our purposes is the disclosure of certain basic topics of our research interests to a broad audience; in particular we want to lead the audience to the reading of geometric shapes that surround us, both from a mathematical and architectural point of view. Then the link between education and research is twofold: through educational activities we offer a glimpse of our research and, at the same time, we do research on teaching techniques.

In the events that we organize, always we leave ample margin to material testing, following the learn-by-doing philosophy. In particular we use origami as a medium to convey some knowledge about shapes; in our activities we consider a great variety of shapes, ranging from origami mathematical models of architectural vaults to (not necessarily easier) origami models of everyday objects. We try to always use a language, which is precise but suitable for the audience to whom we address on each occasion, simplifying contents without trivializing them and hinting at possible research developments.

To exemplify our work, we will describe especially the activities carried out within the European Researchers' Night, which we attend for years and the participation in an origami art exhibition (“Universes of Paper”, organized in Turin (Italy) by the Japanese culture center YoshinRyu). We will show the variety of approaches that we have created to disseminate research and educate the audience, specifying in each case to which target the experience is addressed, the educational goals and methods. In particular:
(i) activities built for groups homogeneous by age and education,
(ii) gaming activities for small groups,
(iii) activities for the general public, not only in form of talks, but especially in form of games and workshops, exhibitions, radio interviews.

For example, in 2015, in one of the activities designed for groups of children, we analyzed the shapes of various types of everyday objects (also considering their sections) and vegetables (in theme with the universal exposition Milano Expo 2015), we used origami folding to represent them in two and three dimensions (in a learn by doing point of view) and finally we used laser scanning techniques to reconstruct and study their images, thus showing, in a simple case, the techniques used in our research on virtual and analytical reconstruction of surfaces. As for activities open to the general public, we proposed origami folds of all kinds: from vegetables to models of architectural vaults that are subjects of our research.

Our experiences have always had a positive feedback and have given us the opportunity to meet and engage educators and teachers, who have guessed the potential of our proposals and proposed in turn some of them to their classes, giving birth to collaborations with our team.

Keywords: Geometry, education, origami, popularization.