Dancing Euclidean Proofs

I appreciated the creator's comment on how dancing through the proofs helps the participant understand the process step-by-step as opposed to looking at a completed proof. I think that doing something physically makes it easier to remember and I was reflecting on how I had to memorize so many proofs for my geometry class but if I had worked through them in an embodied way, it would have been easier to remember them. 

"As we embody mathematical entities, the dance becomes symbolic of mathematics as humanity and humanity as mathematics." This quote stood out to me in the article because I like the idea of mathematics being connected to human history and something that every person can participate in. In the other video we watched about Labyrinths there were testimonies from a couple participants who said they had a lot of fear around Math but doing something embodied opening their mind to the idea that Math could be accessible and enjoyable. 

I think including embodied practice is a fantastic idea in a Math classroom. I was thinking that even counting on our fingers is an embodied tool many students use - but there's actually some prejudice against it sometimes! I think with high school students it would take a little bit of work to get their buy-in as they may be concerned about what their peers think or about looking silly. Another obstacle is that it takes time/money - especially if you want to take a class on a trip to the beach for example. Also, it would be important to make sure it was accessible to all students. 

Euclid and Beauty?

 

• Why is Euclid and Euclidean geometry still studied to this day? Why do you think this book has been so important (and incredibly popular) over centuries?
• Is there beauty in the Euclidean postulates, common notions and principles for proofs? How can we define beauty if these are considered beautiful?

Euclidean geometry has stood the test of time. It is still studied today because it is still true and I think this relates to the second question. There is beauty in the postulates and axioms because it so concisely summarizes these mathematical "truths". Philosophically, there are ideas in mathematics that are absolute "truths" that must remain true anywhere (2+2=4) and I think that is a beautiful aspect of Math. Humans innately know that combining two and two equals four. And in some ways Euclid's Axioms are similar. For example, drawing a connection between two dots is a line. It provides a foundation for more mathematical curiosity and discoveries when there is a set of principles relied on. "Euclid has handed down methods for the clearsighted understanding of these matters" (last page of the article).

Perhaps this is a more spiritual perspective, but I think beauty is something that resonates in our souls. Nature is beautiful because it connects us to the earth and what is alive. Music is beautiful because it can evoke emotion in our souls and transport us to a different time or space. I think Mathematics is beautiful because it connects us with ideas that resonate - they just must be true!  When we read Socrates, I think this was the point he was making - that anyone (even someone who hadn't been exposed to math) could be taught a proof because it expands on these fundamental ideas that resonate with people.

Was Pythagoras Chinese?

I thought it was interesting how Chinese historical documents referred to Math as art whereas the "Greeks saw math as a philosophical pursuit" (p.210). There was a greater focus on logic and proving steps which perhaps lines up more with Western thinking and is a reason for why Greek mathematicians have been celebrated and prioritized more in our culture. It does make a difference if we acknowledge non-European sources of mathematics because it gives students opportunities to explore mathematics with a different lens. I think it is important to celebrate thinkers from different cultures because we will likely have students from diverse backgrounds in our classes and it matters that we directly and indirectly communicate that all our students can pursue their goals past high school. If we only celebrate Greek mathematicians what are we saying to our students about their abilities to succeed in STEM subjects?

I think the naming of these theorems has immortalized these Mathematicians and contributes to the white-washing of history in our schools. To name other people in various cultures who also made these discoveries is a good step in acknowledging that European culture is not superior. I discovered that 17th-century French mathematician Blaise Pascal is credited with the number pattern but it is much older. In the 11th century, Chinese mathematician Jia Xian had a representation of the coefficients for binomials.  There is prejudice against Asian culture in Canada and that can be traced to our colonial roots. I think it is important to deconstruct those ideas by criticizing even the small things like what names we were taught in school. History is important and I was only taught one side, I hope to do better for my students.

Pythagorean proof videos

https://www.youtube.com/watch?v=CAkMUdeB06o

https://www.youtube.com/watch?v=vbG_YBTiN38

Assignment 1 Presentation Reflection

Presentation Slides

Presentation Notes

I really enjoyed doing some research on the history of pi and it gave me some ideas about how to introduce the idea of pi to my students. It is such a fascinating Mathematical discovery and I think discovering it the way ancient people did is a great way to engage with students. Doing this presentation was also a good lesson in time management. I thought 12 minutes would be the perfect amount of time, but I think having longer would have been a good decision in hindsight. Teaching Math that is rooted in history encourages the discovery process in classes. Related to this question: in different parts of the world ancient civilizations estimated the value of pi and how exciting that my students can continue to have the discovery.