Re: Dancing Euclidean Proofs!

I have always thought of proofs as something very logical and routined and I like that aspect of it a lot. The structure of proofing something has its beauty in the form of clean lines and clear step-by-step procedure. However, dance to me is very soft and indirect. Proofs to me are like the school of Bauhaus in design, it's very logical and clear-minded with very little warmth to it. 

After reading the article, especially after watching the dance itself. I felt the warmth and logical beauty of proof through the dance itself. More accurately, I think the movement of the human body is a piece of art itself. 

I find it's fascinating that we can use our legs and arms to "prove" such complicated proof. The rhythm of the dance mirrors the logical side of the proof, it's planned with thoughts but flows so seemingly. 

For non-math people, it becomes so much easier to understand the basic concept of the proof through the use of our own bodies. 

I was also surprised to realize the natural symmetries of our body which is very mathematical in some ways. In conclusion, I appreciated the fact that they used the form of dance to show the beauty/logical thoughts behind proofs!

Re:Explication and commentary on a poem about Euclid (and a parody of it)!

 Euclid is often referred as "the father of Geometry". Geometry exists everywhere in nature, it is the most bare version of beauty. Euclid uses math to show the beauty of nature through the eye of geometry, he also used nature to explore the beauty of mathematics. These two things are naturally inseparable. Euclid's vision on geometry opened all of ours eyes, he created mathematical language to express the beauty of geometry around us. He had a pair of eyes to see through things and noticed the bare bone of lots of things that are related to math. 

Thanks to Euclid, we were able to use math to express/sketch the things we see in this world. We were able to document a lot of historical events using math! 

From the first poem, it seems like It's Euclid who lifted the veil of mystery of the mathematical behind all the natural beauty. The harmony of nature and math was all along there waiting for humans to discover it, and Euclid noticed it. The gate of math then revealed at that moment. Time never stopped, nature never waited for anyone, nature takes its course and it seemed like Euclid was the savior of the dark time of math and opened the gate of pandora's box of mathematics. 

The second poem seems like is criticizing the prasie most people had towards Eulid. It aruges that beauty is in everyone's eyes, math belongs to all of us. No one could be the maker of nature. In other words, no one was the maker of mathematics. Math has been always existed among us, in our day-to-day life. Math is like the air, we breath in and out every day. 

Maybe it's a bit off the topic, it reminded me of a movie called Prometheus. Who is the God, who made us? and, who made them? Who made this world and who created the nature which is incredibly beautiful and mathematical? 

Why do We Teach Math History

When talking about history, I think most of us would have a sense of curiosity and admiration. Reading about the history of math would give us a claerer view of "whys" and "hows". Teaching the history of math will help students to explore the "whys" behind the math we are talking about today, letting them to appreciate the ins and outs behind all the formulas.

I would think students who don't like math wouldn’t take any interest in learning the history of it, but if educators could introduce math via the medium of teaching history, students might take another look at what is math in a different perspective. Math was created from our daily lives which is closely tied to human history, students should be able to notice the beauty of math from learning its history first. I think one of the most common reasons that math was not the most liked subjects in school is because it seems so far away from our daily life, students think there is no use of math. However, it's actually the opposite as math was created from people for practical purpose in their daily lives. Teaching students about it would hopefully help them to see the importance of math and math education. 

Re: Constructing a Magic Square

 This question reminds me of Sudoku I used to enjoy playing. 

To start with the first number, I decided to start with the number in the center. I picked 5 as my first tray-on number for the center number since it's the middle number among 1-9. Since now the middle number is determined to be 5, we know that A,D & B,C should be from the following numbers, 

15-5=10

1,9

2,8

3,7

4,6

Then I tried to put 9 on the upper right corner then realized that it won't work since the number is too big that there won't be so many options left for other spots in the square. Then I tried to put 9 in the middle spot on the top row, then I solved the whole squre. 

See below, 

Re: Research online the significance of the Eye of Horus and unit fractions in ancient Egypt.

    The Eye of Horus reminded me of the pineal gland in our brain which in some regions was called the "third eye". The pineal gland looks like the Eye of Horus and it's the part of the human's brain, the primary function of the pineal gland is to produce melatonin. Melatonin has various functions in the central nervous system, the most important of which is to help modulate sleep patterns. It's interesting how I personally take melatonin sometimes when having trouble sleeping. 
   
     The human pineal gland grows in size until about 1–2 years of age, remaining stable thereafter, although its weight increases gradually from puberty onwards. The abundant melatonin levels in children are believed to inhibit sexual development, and pineal tumors have been linked with precocious puberty. When puberty arrives, melatonin production is reduced. That's why in some cultures, "the third eye" is considered as the symbol of purity and soul. 

    Interestingly enough, there is some math behind this as well. the Eye of Horus was thought to be used by the ancient Egyptians to represent one divided by the first six powers of two

The right side of the eye = ​¹⁄₂

The pupil = ​¹⁄₄

The eyebrow = ​¹⁄₈

The left side of the eye = ​¹⁄₁₆

The curved tail = ​¹⁄₃₂

The teardrop = ​¹⁄₆₄

This reminds me of the golden ratio as well just with different base numbers, which is essentially everywhere in our lives. 

Re: Reading Article Was Pythagoras Chinese - Revisiting an Old Debate

 •Does it make a difference to our students' learning if we acknowledge (or don't acknowledge) non-European sources of mathematics? Why, or how?

Yes, most of math theorems/theories are similar across different cultures. However, they are not totally the same/duplicate of each other. Every culture has its own perspective in terms of understanding the theorems and the purpose of developing the theorems are also different. I think it's important to let students view/understand the same theorem from different perspectives will help them to foster the ideas into their more practical learning. As Canada is such a multicultural country, It's important to introduce non-European sources of mathematics to the class so that students will learn to appreciate the versatility of mathematics around the world. Mathematics is truly a great lens to see the world not only mathematically but also historically! 

•What are your thoughts about the naming of the Pythagorean Theorem, and other named mathematical theorems and concepts (for example, Pascal's Triangle...check out its history.) 

I personally don't feel it's wrong to use someone's name for the theorem, but It can mislead sometimes as that person might not be the first one who discovered the math behind it. However, as we are teaching/learning in a western country, it's understandable to first introduce the western version of the theorem which makes it's even more important to share the non-European sources of mathematics in class. Sadly, schools most likely only introduce westernized mathematics in schools in Asian countries and forgot about they have their own history of mathematics! We should at least introduce them to the students so that they are reminded of their roots which should be embraced by people all around the world. Math is not just some formulas that were recorded in books, it's rather a part of the history that witnessed the development of cultures and human beings. Math doesn't belong to "someone", it belongs to all of us!

Re:Ancient Egyptian 'algebra': The method of 'false position' (estimate, check, adjust)

 

Amy just got paid from her part-time job working as a sales assistant in a clothing store. Her paycheque for two weeks was $1500. Her friend Sara asked her how much does she spend on her outfits, Amy answered "I don't know how much exactly but the money I spent on clothes is half of the money I spent on my food and rent, and I already spent all of the money I got from my current paycheque." How much did Amy spend on her outfits? 

Modern Solution: Let x be how much Amy spent on her outfits. 

x+2x=1500

3x=1500

x=500

False Position: Let x be how much Amy spent on her outfits. 

Try x=100, x+2x=100+200=300

We need the answer 1500, which is 5 times as big as the current answer, so x must be 5 times as big as the trial number. (100*5=500)

Check: If x=500, x+2x=500+1000=1500