Dancing Euclidean Proofs

 Watching this video of previous UBC students interpret Euclidean proofs was very intriguing! I was really impressed that these students were able to portray these proofs in such a refreshing, artistic way. This project reminds me of other themes and takeaways I have drawn so far from this class, which involves the humanity and art behind mathematics. While we have the privilege of taking a class on math history and being able to dive deeper into the culture and innovation behind mathematics, not many people consider these factors, so to see mathematics with such livelihood and art is really fascinating! 

With that being said, one of my biggest takeaways was the imagination that it took for these students to create this relationship between Euclidean proofs and the body. Math can be such an abstract, difficult concept to understand, so the fact that these students were able to imagine these concepts in a completely different form is really impressive.

Another interesting takeaway was the intuition behind the thought processes and planning of this choreography. I found it especially interesting in dance 1, because the dance was choreographed so that if you are following along, you can see a creation of 2 imaginary circles intersecting. I think this must have taken a lot of thought and diligence to plan out!

The third thing that I found really impactful when reading was "this, for us the typical experience of making sense of mathematical proofs, is quite different from what we felt as we choreographed and danced. As we danced, we were active agents responsible for the making and understanding the representation." I found these words really reflected the learning experience of mathematics. Many people often struggle with mathematics because they do not understand other's proofs, or cannot grasp why it works. Being able to put yourself in a situation where you must be responsible for the understanding of the representation will allow these students to grasp these concepts on a much deeper level. This idea reminds me of learning in general. When I was in grade 9, I had a really good understanding of mathematics, and I consistently helped my peers and friends in class. When my teacher approached me, she was really happy that I was able to teach others these concepts, because this reflected that I truly understood the topic! 

Overall, I think the dancing of euclidean proofs is a really unique concept, and reflects a lot of creativity, intuition, and overall a very deep understanding of the topic in order to portray it so beautifully! 

Assignment 1 Reflection

Looking back at assignment 1, there were a few things I found particularly interesting while researching this assignment.

Firstly, I found it really interesting that the "As I Was Going to St. Ives" is actually a word problem that dates back thousands of years ago. This word problem was solved by Ahmes through his Rhind Papyrus, and then later circulated again during Fibonacci's time! I find it fascinating that this answer had appeared almost 30 centuries later, and we still know it today! It is really neat to think about how long knowledge can stay and translate into our current societal contexts. 

Another thing I found really interesting was exploring this ancient Egyptian method of multiplication. I remember Susan going over this method in class, and I really loved how simple it was to understand, and definitely can foresee this being a really useful alternative method for students that have trouble learning multiplication/division. 

Upon our research, a really interesting takeaway was the use of the Abacus to execute arithmetic. It was really neat to learn about this ancient European method, and that it is still actually used today in some countries! The difference in teaching techniques that ultimately results in the same outcome is fascinating to me, as there are many alternatives! I would never have imagined as a young student learning mathematics that there are so many different ways to learn, so it is really interesting to think about how these methods have been taught in the past, and how we can employ these alternatives to assist our youth in learning today.

Euclid Poems

Euclid is a famous geometer and one of the most prominent mathematicians of ancient times. He is best known for his work, The Elements, which is a compilation of knowledge that was used as a primary resource for teaching mathematics for 2000 years. Many of these mathematical concepts and proofs that are found in this piece of work lay the foundation for geometry as we know it today. 

My interpretation of the first poem, Euclid Alone Has Looked on Beauty Bare, appears as an ode to Euclid's findings. The capitalization of "Beauty" in this poem makes me think that Edna is personifying this concept of "beauty" and giving it a connotation in relation to geometry. She is effectively describing Euclid's significant advancements as his way of viewing "Beauty" in it's truest form - bare. My interpretation of this is that Edna is highlighting how Euclid was able to see things about mathematics that others were not able to, and he was able to produce proofs and concepts that were not yet discovered. I think Edna is using this poem to really showcase and glorify Euclid's advancements, as "Euclid alone has looked on Beauty bare" appears to put Euclid on a pedestal as he is the only one to achieve this, and he did it all by himself. 

I think the second poem may be criticizing Edna's "Euclid Alone Has Looked on Beauty Bare". The beginning of this poem, first quoting Edna's, and then questioning the ideas she had brought up "Has no one else of her seen hide or hair? Nor heard her massive sandal set on stone?" makes it seem that the author does not share the same views as Edna. I think this author does not believe that Euclid should be glorified this much and given this much credit for his work. In my research, I read that The Elements was likely not a result of Euclid's direct work, but actually just a comprehensive compilation of many advancements at the time. Since there is this theory that Euclid's The Elements is not a product of his own proofs, I think this poem may be alluding to this factor that Euclid does not deserve all of this credit. This idea reminds me of previously-explored ideas in this class, such as if Pythagoras was Chinese. I think the goal of this second poem was to shed light on the fact that we cannot attribute advancements like this to one sole person - it is likely a product of collaboration and other individual's previous findings that allowed Euclid to produce his legacy.