# 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.