Yesterday, we conducted a maths workshop in the «Colegio Agave» (Huercal de Almería), together with David Crespo, Pilar Gámez, and other teachers.
One interesting activity was to cover a float (a torus) with regular polygons of 3D Polyfelt. How many possible combinations are there? Of course infinite. It depends of the size of the pieces (or the size of the float), the regularity or the smoothness we want to get, etc. Note that the flexibility of felt, increases the number of solutions. We think that this is a good project to investigate in secondary school.
Students interested on this subject should look for «tessellations» of the torus. One could for instance, compute the Euler characteristic (vertices-edges+faces) of its own tessellation, and see that it is equal to zero.
We will come back to this post and complete it with some pictures and possible projects to realize. Other surfaces, like cones, cylinders or hyperbolic saddles could be also interesting to cover.
[Update May 19th, 2013: See the experience with some calculations here.]
We next leave a short video with a few moments of the workshop, the students enjoyed very much with many of our favourite manipulative games.