Last year I had the amazing opportunity to spend some time in France, Dijon, capital of Bourgogne. I attended Computer Aided Geometry of Curves and Surfaces with Image Recognition (CAGIR), an intensive programme of the European Union LLP Erasmus for selected math students from Italy, France, Spain, Poland and Belgium.
In these few lines, I give you an outline of the course, the main subjects and tools discussed and used (for more details you can read other posts in my Blog – at the moment available only in Italian).
CAGIR is an inter-university course devoted to teaching geometry and computer graphics with applications in art, medicine, image recognition, and everyday life. This innovative programme consists of 60 hours of lectures, tutorials and laboratories in 2 weeks, led by an international group of mathematicians.
The main topic of the course was Differential Geometry, a mathematical discipline that studies the evolution of geometric entities through the analysis of their individual parts. Applications of this research area are countless: e.g. in the last football world cup matches, some differential geometric techniques were used to trace the path of single football players and measure the distance they had run.
During the course many internationally renowned mathematicians have showed us theorems, lemmas, propositions and definitions that make up the theory. So we studied minimal surfaces, examples of Riemannian Geometry, different kinds of curvature, and many other very interesting concepts.
Besides all these theoretical studies, we participated in several lessons of calculus and computer science. So, we examined in depth some powerful software, like Java, Matlab, Mathematica, and Pov-Ray. In particular, I very much appreciated Pov-Ray, a useful tool for ray-tracing, that allows to draw geometric figures putting a camera, spotlights and light sources in a virtual dark room. That way beautiful figures, like the one in the picture below, are generated through scripts exploiting the potential of Pov-Ray.
Another fascinating point of CAGIR was the exchange of ideas: instead of traditional lectures, we attended interactive lessons. Teachers did not care if we understood everything of their seminars, they just wanted to leave us with an idea. With this approach, students were motivated to think quickly and fill up gaps of knowledge through team-work. In fact, at the end of every topic, we were divided into multinational groups in order to have each country represented in every group. During these problem sessions, we discussed the topics covered in class and did the exercises. So, I really appreciated experiencing how students of other nationalities approach their studies and received confirmation that mathematics is a universal language.
In conclusion, I was very happy to attend CAGIR. Mathematics brings together different people from all over the world. This is a big achievement for humankind.