Euclidean Poetry

It appears that these poets are basically comparing Euclid to some sort of a math messiah. The capitalization of Beauty implies that it may be a metaphor for God, which Euclid has somehow brought to earth. Also the references to Greek mythology, as well as biblical languages, and references to paeans (which to my knowledge are like church hymns) suggest that Euclid's work is being highly appreciated. 

I argue Millay was trying to convey in her poem that these fundamental principles being built into logical arguments is "beauty" in its purest form. There is no debate about how these principles work and they will always work. When Euclid first introduced this type of reasoning to the world, he introduced the world to pure "beauty". 

On initial impression, it appears to me that Kramer is suggesting that even with Euclid's contributions, we still do not truly see "Beauty" in all its glory. In my personal view, I think that he is suggesting how few people, and maybe even Millay, herself, truly understand the workings of Euclid. Also how much easier it is to "see Beauty clothed" which I believe implies that we see and understand the aftermath of these discoveries/principles, but we don't really know them truly. 

Just some of my five cents.  

Response to: Was Pythagoras Chinese

Let's Acknowledge Non-European History 

I think that if we are to credit European math history it is also important to credit non-European math history. When I was first debating this stance in my head, I thought that it didn't really matter to students, especially if history is not the focus of the math lesson. But then I thought, even the names of these Greek mathematicians are incredibly dominant in how we teach math and these European names really do matter (even if it is easy to discount their importance to students). I look back to when I was in school and I was fascinated with Ancient Greece, and I would be so excited to learn about how the math was present in this history as well. But if I had known about the contributions from other cultures, would I have also taken fascination with them? I think it is kind of unfair that these European mathematicians get this seen more often. I think that giving credit to all the various contributors is important, as well because it recognizes various cultures and demonstrates the commonality of human civilizations. 

Naming Theorems 

At this moment, I feel annoyed and maybe frustrated with all the theorems that give credit to a person who contributed to them. I think these feelings stem from the fact that it is so difficult to just give one person credit, especially when it is not clear if they were necessarily the true discoverer of these ideas. Then, I think what else would we name them? I suppose practical names would be beneficial. I think in class, a peer told me that in China the equivalent of the Pythagorean Theorem is called the Gou-go Theorem which means the Short-Long Theorem. I think that names like these are more practical, fair, and universal. But then what do you do for theorems where there isn't a simple descriptor name, I'm not totally sure -- maybe just make something up, vote on it?  

Reflection on Assignment 1

Like other concepts in this class I think that it is so amazing that these mathematical ideas have been around for so long and in areas where it is unclear and mysterious how they came to these conclusions. I suppose I enjoy the idea that student that do not necessarily enjoy the typical math classroom, may really take interest in these types of lessons. There is more of a curiosity element to it. I also felt some frustration when trying to solve the ancient way because it was very unclear, which is similar to the feeling that I have when faced with a difficult proof. At the same time I think I would really enjoy having student do a similar activity and teaching similar concepts that we are learning in this class. These historical techniques seem to also appeal to"practical" math, while also having a more personal touch, which many students seem to crave. I hope to help my students appreciate math more with these concepts. 

Egyptian Fractions

I suppose the benefits of using unit fractions in ancient Egypt were revealed in class. It was an easy way to spilt meals amongst workers. I think it would also be possibly used for things like dividing property or inheritances, as the word problem suggests. 

The use of unit fractions today is less obvious to me. I suppose it could be used a tool for doing mental calculations. I know I sometimes figure out what is 10% or (1/10) of something is as a reference point for things like tipping or calculating discounts. I also looked up Egyptian fractions on wikipedia and they
suggested that today they are useful for rope burning puzzles. I think they could also be used like the Egyptians used them, when my family is dividing food, sometimes like a lasagna or a cake or a kit kat bar (when there are three of us), we will sometimes do something similar, where everyone get approximately one size of the first portion and then whoever wants seconds gets approximately a second portion of a different size.   

Here is some of my work for the horse inheritance puzzle: 

Solving Pythagorean Triples in Modern and Ancient Ways

 Here is the link to Heesung's and I's assignment.