Response to "Dancing Euclidean Proofs!"

Once again, I am impressed and moved by the perfect combination of Math and Art in this course. I really enjoy the beauty this video brought to me, especially when I know exactly what the dancers are trying to convey. The background music with a little sound of waves is soothing. The dance on the beach sand is expressing some classic propositions from an ancient mathematical and geometric treatise. What a wonderful feeling! 

During the decision-making processes in creating the dances, three co-authors (Milner, Duque, and Gerofsky) came up with many good ideas. There are two of them stood out to me. The first one is that the authors decided to use both arms to spin in circles in Dance 1. For proposition 1, we know there is no diameter in Euclid's original diagram, however, they creatively found a beautiful solution to the imbalance problem. Moreover, with "extra" arms they naturally made an equilateral triangle and a fluid dance. The second one is that the authors decided to dance on the beach in order to draw in the sand to record the movements. Like they said, the new element-- Land, added beauty and more possibilities. When dancers disappeared after the dance, the trace left in the sand reminded me of a famous painting "The School of Athens."  In the painting, Euclid is drawing a theorem for his students with a compass. I somehow entered that painting as I was looking at the trace in the sand and hearing the background music. Just like the authors say in the article that "as we dance the proofs, and as a live audience might view them, we somehow enter the page." (p.243)

" The body does not move in a vacuum, but in response to stimuli from the land and place."(p. 245) Using the environment as part of the proof is a great idea. Old civilizations found wisdom from the natural environment. I think people naturally like to feel connected to nature. When I was young, I always drew trees and mountains in my pictures. Even though I couldn't explain why at that time, I felt trees and mountains are indispensable. 

To demonstrate the propositions of Euclid's Elements through movement and dance was not easy. Many things and details related to proofs and choreography were needed to be considered. But at the same time, the entire process must be full of interesting ideas and beautiful moments.