I am working on a unit plan dealing with tranformation geometry level secondary education.
Students do enjoy creating those visual transformation but
I am trying to figure out what could be a nice project with transformation geometry... that can answer a dilemma existing in the real life and that can be appealing to a teenager.
NEW EDIT: I have been reading/prospecting the very interesting link below. the central point is symmetry and transformation. The math of it seems to be focused on the creating groups (i.e. group symmetry, the "17-wallpapers"), how symmetry is fundamental in physics, defining or constructing a transformation or a composition of transformation.
So far, I envision as final project where students create an expository gallery of (let's say) 6 tessellations. Starting with some tessellations involving simple plane-figures and simple transformation up to having a final tessellation involving a composition of figure (maybe a pentagon as mandatory to create a constraint as it does not "tessellate by itself"). For each tessellation, 2 parts: The 1st part the image of the construction phases done with geogebra + the description of those of the transformation fitting with mathematics phrasing, 2nd part the creative result and a paragraph explaining the "beauty" of it. The "beauty of it" would essentially be about describing the symmetries and (eventually, if it is not too complex for students) the operation under this group. Students will then assemble those in a gallery or in an electronic portfolio.
So far this is what I heading to ...
Symmetry (and tessllation) is a first time encounter for me. What do you think about what I am proposing? What could the drawbacks be?