Eye of Horus and Unit Fractions

 The Eye of Horus is a popular symbol to ancient Egypt, representing protection, health and restoration. 

From my research, it appears that the common unit of volume was called hekat, a term we have also seen in other ancient Egyptian texts and word problems from previous classes. For smaller amounts of the hekat, this volume measurement could be expressed in 1/8, 1/32, 1/16, 1/4, 1/2, and 1/64, which was represented by the symbols below for each unit fraction. 

Because these unit fractions were written using symbols that depicted the Horus Eye when put together, these unit fractions were known as Horus-eye fractions. The story of the Horus Eye in Egyptian mythology included Horus's eye being damaged and wounded by Seth. Thoth, commonly known as the originator of mathematics, was able to heal Horus' eye with his fingers. One theory shows that the eye's sum of the unit fractions was just short of 1 by 1/64, and this is the part that Thoth contributed to heal the Eye of Horus. This is a really interesting story that ties ancient mythology and unit fractions together! 

An example I can think of where numbers have meanings or special stories is anniversaries. Anniversaries can be a very meaningful, special day for couples in relationships, and this is celebrated on a specific date each year. This tradition attaches a special event/memory to a specific number. I actually have a friend that has had multiple relationships, and always makes sure that her anniversary date with her new partners do not overlap with previous anniversary dates from previous partners. This goes to show how much attachment and meaning people can associate with numbers! 

Magic Square

  This magic square problem was really interesting to me because I remember solving problems like this in elementary school! These fun, math problems really get your brain thinking, and it's interesting to think about how we actually solve these. Here is my process of solving the magic square:

Initially, I had this answer, which was fairly easy to get, but then I realized that one of the diagonals do not add up to 15. My initial process was to start with 1 in the top right corner, and then use the larger numbers on the spectrum (8 and 9 in this case) to fit in the row and column that align with 1. Using 9 and 8 and then going from there, I was able to solve this square quickly. 

After initially solving the magic square, I knew that I could keep the same number combinations (i.e 8-3-4), but I just needed to re-arrange them so that both diagonals would add up. Given this, through trial and error I was able to figure out that both diagonals needed to include 5. Because I already knew the combination 6-5-4 would work for one of the diagonals from my initial trial, I inputted this diagonal first and put 5 in the middle so that it would fit in the second diagonal. From there, I had figured out the second diagonal needed to be 8-5-2 through trial and error. Once both diagonals added up, I was able to fill out the corresponding number combinations from my first trial. This was how I solved the magic square! 

Was Pythagoras Chinese?

 Personally, I think it is very significant to acknowledge the sources of non-european mathematics, since all of our history is mainly centered around Europe. However, as a young student learning about Pythagoras, I'm not sure that it will make a big difference to them, because I don't think many of them are aware of the euro-centric views of history and the world yet. I think this is definitely worth sharing to a classroom for young students, I am just not sure how many students may actually find this relevant to their studies. In my opinion, I believe that taking time to explain the "why", such as why is it important for students to understand the Pythagoras theorem, is much more beneficial and significant to young minds. 

In terms of my thoughts for the naming of the Pythagoras theorem, I do think it is important to name theories, just because it adds more humanity to mathematics. Understanding that an individual was able to discover this great theory, or had this revelation that progressed mathematics, is important to our history and culture surrounding mathematics. Where would we be today, without acknowledging the great works of Albert Einstein, or Isaac Newton? Although it is obviously unfortunate if a theorem is named after someone that actually wasn't the original creator, I think it is more about acknowledging the hard work that is behind a theorem. With the discussion regarding if Pythagoras was Chinese, I believe that it is more important to explore the discussion and the different findings that came to be from the Chinese culture, rather than dwelling on the fact that someone may had done it first. 

Word Problem - False Position Method

Ron borrowed X amount of money from Harry, and promised to pay it back in 3 months. 1 month in, Ron paid 1/5 of the amount by paying for Harry's food. At the end of the 3 months, Ron gave Harry $96. What was the original amount that Harry lent Ron?

x = money lent to Ron 

x - x/5 =  96

First, we'll try x = 10

10 - (10/5) = 96 

10 - 2 = 96

8 ≠ 96 

Since 96 divided by 8 = 12, the correct answer should be 12 times our trial number, which was 10. (12 x 10 = 120)

120 - 120/5 = 96

120 - 24 = 96

96 = 96

Therefore, Harry lent Ron $120. 

A Man Left Albuquerque Heading East - Babylonian Word Problems

 My initial impression of this text is filled with fascination as we have such a rich history of word problems! It is really interesting to have evidence of history dated back over 4000 years ago, and to understand the differences in what societies did back then compared to our conventional methods today. 

I do think that these problems were practical, because they were based on real world applications that individuals may have faced at the time, such as dividing up an estate in the case of someone passing away. The word problems that we see of this era are typically centered around harvesting, agriculture, and other everyday activities that were present during this time. I am not too sure how to interpret generality in this context, but I do think these problems are helpful for understanding and learning mathematics.

I think the concept of abstraction is typically present in word problems, and I can noticeably see that here in these examples as well. Although the problems are centered around real world applications, I believe they are designed for the purpose of teaching mathematics, which is why they can appear far fetched and abstract. Furthermore, I definitely think that I am biased when writing this post based on my familiarity of modern day algebra. I am sure that different mathematical methods and approaches worked for different civilizations, and these are my ideas based on our civilization today. 

Assignment 1

 Link to Margot and I's presentation on As Ahmes was going to St.Ives

https://docs.google.com/presentation/d/1Wqyy652vSVV6qoujA1cfXZ33vjY7iq_9q8HN_-qXx14/edit?usp=sharing