Discovering Group Theory, Day 1

Topics:

What is symmetry?
How do we quantify it?
Symmetries of polygons.

On Day 1, we looked at examples of polygons and tried to rank them based on their symmetry. First we had to come up with a sensible criteria for something to be symmetric, which we agreed had to do with the number and kind of operations which leave the polygons looking the same. Then as a class we used those criteria to rank the polygons based on the number of such possible transformations, which we found to be rotations and flips.

Students investigating symmetries of polygons.

Various polygons and observations of their axes of symmetry. — Summarizing the observations from the investigation as a whole class.

Materials: Construction paper and some magnets.