- What happens when we have two mirrors?
- What if the mirrors are parallel?
- What if instead they intersect? What if we make the angle between them larger or smaller? How many images do we see?
- Try the activity and followup here.
- Rotations can give powerful effects, especially when you combine multiple rotations or introduce other visual effects. See David Roy’s work in wood and John Edmund’s “strobe animated” 3d printed sculpture.
- Playing with this app can give you some good experience with rotations and reflections.
- With one center of rotation and possible mirrors that intersect at the center of rotation you will finitely many symmetries in patterns called rosette patterns. Rosette patterns can either have mirror symmetry or not and are completely characterized by the order of rotation in the image.
Frieze Patterns and Wallpaper Patterns
- Translation (moving or stamping out an image) in one direction or parallel mirrors can create a frieze pattern.
- If there is translation in two directions, we get wallpaper patterns and there are only 17 of those!