Oct 20 - Eye of Horus

 According to Egyptian mythology Seth (Osiris' brother) killed Osiris, and Horus, who was the son of Osiris, fought and killed Seth, but also lost his eye in the battle. Part of his "eye" were restored by the god Thoth.

Egyptians used fractions to measure grain and these fractions were parts of a hekat, which is the Egyptian unit measure for grain.

This is the only information I could find about it after reading parts of the books found in the "References" section below. I found it interesting how the God gave back his eye, as if he didn't deserve to lose it. The eye and its fractions are connected to grain, which is an important element of their sustainability, perhaps as a reminder of justice.

As for myself, I grew up in a superstitious household and culture and the number 13 scared me a lot, as it was supposed to bring bad luck. Even up to this day, whenever I see it I have to remind myself that it's just a number and it's all mysticism, and that it has nothing to do with the cause and effect of daily events.

References:

Great Scott Publishing. "Egyptian Hieroglyphs. Eye of Horus." https://www.greatscott.com/hiero/eyef1.html.

Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, p. 40, 2002.

Oct 19 - Magic Square

At first, we realize we cannot have a big number in the center, because as soon as we add another next to it, it can go over 15. I.e. 9 and 8, 9 and 7, etc.

Therefore we place the big numbers on the edge, in the center columns, away form each other. Then it was kind of trial and error to see where the others fit.

Solution:

6 1 8

7 5 3

2 9 4

Trial and error attempts:

1 8 6         X 9 X

X 9 X         7 X 8

X X X        6 X X

 

X 9 X         X 9 X

7 1 X         7 5 X

X X 8        X X 8  ----> here I realized I'm on the right track, and then played with the rest to get the solution

 

Oct 13 - Was Pythagoras Chinese?

I think it does make a difference to our students' learning if we acknowledge non-European sources of mathematics. The main reason is having someone to relate to. While, as adults, we don't necessarily look for role models, we forget that children do. Showing how mathematics was developed in each culture, can have long lasting impacts on someone's identity in terms of how they relate to mathematics. Knowing that your ancestors were hot on the subject can bring a sense of belonging and connection to the subject. Therefore, teaching mathematics history in a classroom that has diverse backgrounds is another avenue for inspiring the students.

I do not oppose naming theorems after the person who invented them. However, I think mathematics would be much cleaner if the name of the Theorem would be suggestive of what it's about. This can be seen in the more modern theorems where theorems are not named after the mathematician who invented them. So I guess instead of "Pythagoras's theorem" we could just call it the "90 degree Triangle-Square relationship" or something like that.

Oct 13 - Method of False Position

The reason the method works is because the equation is linear so any scaling of x will scale the answer.

 As for my own problem: Tutankhamun thinks of a number. Then, he adds to this number only one third of it. He gets 28. What is the number Tutankhamun thought of?

Oct 7 - Babylonian word problems

I believe that word problems can be used for both training students to use some methods, as well as actually solving real world problems. For the former, we can use the example of (a+b)^2. We can definitely show the students the algebraic, or even the geometric derivation like so:

Just seeing the formula, however, wouldn't give the students the skill in performing mathematics with it. Therefore, apart from the usual algebraic manipulations, we can use concocted word problems such as putting a frame around a picture:

Source: https://i.ytimg.com/vi/n_4t9JnwE9s/hqdefault.jpg

 While the practicality of this problem is nonexistent, it does give the students more practice, and builds skill. 

 Generality, and abstraction are very important aspects of mathematics. Another example that can be brought up here is whether teaching factoring is valuable. Factoring, the way we do it in high school, does not generalize and it is not connected to mathematics in its general picture. Whether we should teach it or not, I am not yet sure.

When it comes to "the idea of 'pure' vs. 'applied' mathematics", from our experience it can be thought of applied mathematics and mathematics that hasn't been applied it. There are several examples, such as number theory (RSA), when mathematics was there for the taking and to be used in real world applications.

The ideas above definitely rely on our familiarity with contemporary algebra, since it's the framework in which we have built the reasoning and general ideas. It could be that some aliens have invented their math in their own way, but the math we have thought out so far would probably match up to isomorphism with theirs.

All of these ideas related to Babylonian and Egyptian mathematics in the sense that humans have been thinking abstractly and making abstract mathematics ages ago, and it's still a continuing process.

Problem 1.2.2 - Presentation - Slides

 https://docs.google.com/presentation/d/1emKksT595cmhzfDsIjIuocaeUOvv6U9Ivim3Q84YFVQ/edit?usp=sharing