The Challenge: Pick YOUR favorite proof, or mathematical fact and illustrate it. What’s beautiful about it? Why do you love it? I really, truly want to know.

Materials Needed: Really depends on your pick! Math conceptsyou could explore with this challenge: Philosophy on Math. Mathematical communication.

And it doesn’t have to be fancy. It can be simple. The runner up for me is probably the triangle area formula. The following, however has to be the winner as even ~10 years after I learned it, if I’m reminded of it, it still stops me in my tracks.

MY favorite proof, and still, to this day, the most beautiful thing I think I’ve ever experienced in mathematics, is a proof for how many spaces are created by n-crossing lines. If you just want the prettier part, here you are. This is the proof:

Here’s even a time lapse:

But (insert math teacher persona here) the REAL beauty is, of course, the idea. Which I did my best to explain here:

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

3.) Construct viable arguments and critique the reasoning of others. How will you convince others that yours is truly beautiful? What must you communicate to them?