Discovering Group Theory, Day 2

Topics:

  • Rotational symmetry
  • Identity
  • Inverse
  • Formal definition of a group
  • Group product

On Day 2, we considered only rotations of various polygons around their geometric centers. After a systematic hands-on investigation and cataloguing of rotations which leave a polygon unchanged, we identified the identity transformations and the inverse of each rotation. The class concluded we the formal definition of a group.

A white board with drawn polygons and lists of the rotations which leave it looking the same.
Cataloguing rotations of various polygons which leave them unchanged.

 

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.

Materials: Construction paper and some magnets.