Symmetry: Smart Phones, Friezes, and Fractals
What is a more interesting way to discuss and explore symmetry in a school curriculum? Sure, we can point to squares and triangles and other shapes and list all the rotational and reflection symmetries they possess. Okay. Umm … What next?
In thinking about symmetry in the school curriculum for an upcoming workshop I decided to explore symmetry in a deeper way.
* Is it obvious that the two-finger swipe one does on smart phone maps should keep pictures of straight roads straight?
* Did you know that there are essentially only 7 symmetry designs for friezes, and 17 symmetry designs for wallpaper patterns?
* Self-similarity is a type of symmetry. Did you know it produces of fractional dimension?
These are just three ideas that are accessible and interesting for high-schoolers. I explore them here.