Dancing Euclidean Proofs

 Hello twins.

The following is a response to the Dancing Euclidean Proofs film we watched in class as well as the Bridges Math & Art article.

One idea that stood out to me was how the temporality of dance contrasts with the "all-in-one-ness" of the images or proofs we often read in math textbooks. The choreography adds an element of time where you can see each step of the proof sequentially build on each other. Scanning through a proof by reading it simply doesn't offer the same allure. Breaking proofs down into their individual components allows a greater appreciation for the methods and ideas behind the proof that are often lost. Too often we see these proofs as just one overarching idea, without recognizing the great amount of thought that went into building each step. This also more closely aligns with my experience with solving proofs. Rarely would I simply zoom through creating my own proof from start to finish. Instead, I would proceed methodically and carefully considering potential next steps in my argument. I also appreciate that the performance was done on the beach. Using nature as the backdrop for a math proof helped the audience connect with the inherent beauty of the argument. It starkly contrasted the typical institutional setting in which math is carried out. This would be an interesting addition to a high school math class as a final project perhaps in a geometry unit. I wonder if there could be other ways to modify the project for other math topics such as graphing or algebra. I would also consider altering the dance to other non-proof examples. There would likely need to be a certain level of maturity for this project to be carried out effectively and I wonder if some of the students may not want to buy in due to its performative aspects. Dancing can be a vulnerable act, especially for a teenager, and I wonder how we could potentially modify the activity to make it more accessible for all students.

Thanks for reading,

Josh