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.

Pamphlet on Symmetry


    QUADRATICS, Permutations and Combinations, EXPLODING DOTS, and more!

    Written for educators - and their students too! - this website, slowly growing, takes all the content Tanton has developed in his books, videos, and workshops, and organizes it into short, self-contained, and complete, curriculum units proving that mathematics, at all points of the school curriculum, can be joyous, fresh, innovative, rich, deep-thinking, and devoid of any rote doing! Let's teach generations of students to be self-reliant thinkers, willing to flail and to use their common sense to "nut their way" through challenges, to assess and judge results, and to adjust actions to find success. (Great life skills!)


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