I teach Geometry to academically talented 8th grade students. Each quarter I assign independent projects to reinforce and enhance the geometry that we study. For example, after studying polygons, the students have an option to research the work of MC Escher and learn about, and CREATE, tessellations. When we look at solids, they build the 5 Platonic solids and answer questions about why there are only five. My favorite is after the kids study volume and surface area they have to create cereal boxes that use less cardboard than Rice Krispies, or whatever cereal they have on their shelves, but have the same volume as the original box. They ultimately write to the cereal company giving a reasoned argument about the environment, cardboard, volume, etc. It lays a nice foundation for max/min when they get to calculus. Anyway, my repetoire for the first quarter, when the kids don't know very much, is somewhat limited. I have them research Euclid and the first five postulates, create some "Islamic" art, and look at topology and the life of Mobius, but I'm not happy with these first quarter projects. Any suggestions???