The curvature and torsion: how to distinguish the shape of a curve (*) 
Introduction
Any moving object describes a curve in space (think, for example, of the curves that birds or butterflies "trace" during their flights). Is there a mathematical "language" to describe the shape of curves in space? Yes, it is the "language" of curvature and, in the three-dimensional case, of torsion. These two concepts are very intuitive and we may introduce them with the help of everyday life situations.
For plane curves we may consider the track of a car and observe the relation between its curvature and the behaviour of the steering wheel of the car.
In case of three-dimensional curves, a natural example is the airplane and its possible tracks.
(*) This work was carried out under the guidance of Professor Jorge Picado from the Universidade of Coimbra, under a grant by the Calouste Gulbenkian Foundation to develop a project for the promotion of Mathematics in Atractor.
Since many browsers are blocking Java nowadays, it was decided to convert to Javascript the original applets of this section. This conversion was carried out within the scope of a support received from FCT - Fundação para a Ciência e a Tecnologia, through FACC (Fundo de Apoio à Comunidade Científica).
Difficulty level: University
