"Dancing Euclidean Proofs" Reflection

Before reading the paper, I struggled to make a logical connection between geometric proofs and dance, and was fairly curious as to why they chose to represent Euclid’s proofs in that medium. As breath-taking as their choreography was, it simply wasn’t the rigorous and permanent style of proof that we’re used to. So, the first comment the stood to me was “our first step was to make explicit for ourselves that rationale for translating these proofs as dance.” And they provided marvellously comprehensive and convincing points as to why it made sense! Though the topic was specific, their arguments are easily applicable to expressing math in any form, available to all types of learners. Their embodied visualization is particularly applicable to visual, kinaesthetic, logical, and naturalist learners, which reiterates that learning math isn’t confined to any learning style, and directly synthesizes a hands-on experience with learning math. 

I find it absolutely striking how clearly the paper demonstrates that math is not the pencil-paper subject that we experience in our classes. In fact, it beautifully articulates that “math done on paper is a representative process that relies on the mathematician’s imagination to reconcile the limitations of representation”, and in that respect I can’t agree with the traditional ways that we’ve learned math because the 2-D communication takes much away from the intricacy and elegance of some topics. In the accompanying video, we can see how embracing Euclid’s geometric proofs with their whole body, rather than just their brain, visibly exhibits their deeper appreciation and perception of the topic. It's quite inspiring how taking geometry outside of the classroom in that way completely modified their experience with it. 

For the entire duration of the paper, I was thoroughly intrigued by their decision-making process. Not only did they have to consistently assess the practicality, fluidity of their dance, and the sequentiality, they were able to adapt to their environment and incorporate that new medium into their proof. As complex as it may have been, filming from a bird's eye view to bridge the gap between the land and their dance displayed their artistic mastery of dimension and perspective, which was something I really enjoyed. I was rather surprised that their challenge with using the land in their proof, turned out to be their biggest asset. By selectively embracing everything that seemed like a challenge, they were able to produce a rather remarkable and memorable demonstration. And, in their paper they eloquently express that “As we embody mathematical entities, the dance becomes symbolic of mathematics as humanity and humanity as mathematics. We are … not just wrestling with but also becoming the mathematics we do”, and that impact of that statement is immense.