Dancing Euclidean Proofs

For your homework blog writing, please read the article linked here and comment on three things that stopped you in your reading or that struck you about the relationship of mathematics and Euclidean geometry to body, Land and movement. Your writing is due on your blog on Tuesday November 17 at 9 PM.

One thing that struck me was the concept of being the proof oneself.  "we somehow enter the page. We imagine ourselves to be like the two dimensional characters in Abbott’s Flatland [1]. While dancing the proofs adds a temporal dimension to Euclid’s original representation, the positionality of the dancers and audience (in the same plane) involves some loss of the third spatial dimension." I think this is quite interesting because when one embodies the proof, one should never forget it. If we let our students do the proof using this method, they would hardly forget it.  As said, " The process of choreographing the dance proofs — making decisions, practicing, memorizing — both transformed and guaranteed the internalization and mental recreation of the proof."

Another thing is that "Black and white photography clarifies what a colour picture might obscure; musicians sometimes close their eyes while playing to focus on sound." This is quite cool. I like that. As it is consistent with the idea of simplicity and focus. When we have black and white images we tend to focus on the essence of the content rather than being distracted by the colors. There are already so many distractions to the eye, and math is about simplicity and art. hence this is quite considerate and useful. When we are doing some projects or presentations we could also use that choice.

Third thing is that "Math done on paper is a representative process that relies on the mathematician’s imagination to reconcile the limitations of representation. Euclid’s proofs, for example, take points to be infinitely small and lines to be infinitely narrow and long. However, the points we draw on paper have real size, the lines real width and length. In the same way, the audience must reconcile the misrepresentations' of our dancing bodies. ”

This is also quite an interesting topic because when we draw 3 d diagrams  for the students its usually on a 2 d surface. Imagination and the reconciliation for the limiataions of representation is an important skill the students have to learn. We sometimes take for granted that they could understand but actually its not! we need to find ways to make them understand. And doing some hands-on activities or acting it out might be a good method.