Response to "Dancing Euclidean Proofs"

One of the goals described in the article is to "make the beauty of Euclid's proofs accessible to mainstream audiences and students of mathematics through the physical beauty of dance" (page 240). I think such practice is very important in pedagogy of mathematics, especially in a time when math-phobia is the norm among general public. The regular mathematics in a textbook is intimidating, even to a math major university student. Using a form that is more popular and more appreciated by the public can reduce the fear towards mathematics, and people can make connection from what they already know about dancing. 

The audience is not the only ones who benefit from such a embodied, performative form of mathematical proofs. The dancers themselves, through "the process of choreographing the dance proofs -- making decisions, practicing, memorizing"(page 244) internalize and mentally recreate the proofs. Recreation using one's own approach/language/tools is the best way to study a complex concept. 

All of the above is possible due to the amazing compliance between Euclidean Geometry and performing arts. It would be almost impossible if anyone try the same approach on topics such as partial differential equations... We don't know if Euclidean had thought about the symmetry of our human bodies when completing his book "The Elements", but geometry really comes from the part of life that is obvious to most of us. And this is the great starting point for math education for the young.