Dancing Euclidian Proofs

 I found it interesting how it took time to choreograph this dance, and how there was a trial and error aspect to it. At first the proofs did not seem to lend themselves to dance, but after changing some base assumptions of how the dance should look things fell into place seamlessly. This embodies the process that all mathematicians go through, where roadblocks keep being hit until we have an epiphany moment that changes everything. This makes me think that not only were they able to dance the proofs, but they unlocked a new way of doing the math. Similar to the invention of symbolic algebra over classic geometric. They felt that things were "off" when dancing improperly, perhaps by dance we could solve some of the stickier problems in math.

I enjoyed the discussion of metaphors. The critique of their bodies not exactly representing the mathematical constructs was something that crossed my mind while watching them. But they make excellent points how our visual representations of math objects is imperfect as well. When one comes to term with the facts that no matter what tools they use, they will be imperfect representations, we can include so many different types of representation. And with these new modes, we may gain new insights.

And I think this idea of imperfect representation is one that is the most applicable to the classroom. Educators are trying to convey knowledge to students, and use a myriad of methods to do so. The words in a lecture, the drawings on a board, the feel of 3D printed shapes; all of these are imperfect yet useful. It is ignorant of us to decide that some modes are more imperfect than others. If I want to say that I tried my best to convey an idea to my students, then I must use all of the tools at my disposal.