Reflection on Eye of Horus and unit fractions in ancient Egypt

 

While gathering information, I found that Eye of Horus is depicted to a Falcon. The right eye of Horus (Ra) represents the sun which serves as good luck, and left eye of Ra represents the moon which serves as protection. The interesting part of Eye of Horus is how Egyptians divided the eye into six parts using fractions and connected those fractions or parts with the five sense and the sixth sense as thoughts. They used  1/2 for the smell,  1/4 for vision, 1/8 for thought, 1/16 for listen, 1/32 for taste, 1/64 for touch. The picture below explains that each part of the eye represents the senses with unit fractions.

             

Thinking about Indian culture, I realize that in Hindu mythology, people consider the sun (Surya) as god brings fortune in their lives. Therefore, some religious people always do Surya Namaskar ( pray to the sun during sunrise)  for good health and wealth. I noticed in India that some people place the symbol of the sun over the doors of their houses and business shops.

Sources:

https://egyptian-symbols.com/pages/eye-of-horus

http://www.landofpyramids.org/eye-of-horus.htm

Magic Square

I used the technique to solve the magic square that I learnt in high school. I know how to do 3 x 3 magic square, but now I use the method to solve 5 x 5 magic square. 

Things to remember while solving magic square:

1. Always start from the center of the first row and fills the box with your starting number.

2. From that box, follow the diagonal upward arrow (only for one box) to place the next consecutive number.

3. If there is no box at the diagonal upper right, then imagine as a box and follow the arrow vertically (downward) and horizontally (left) to the last empty box of the magic square.

4. If the box at diagonal arrow is filled, then follow the arrow downward(only one box) without using a diagonal arrow.

5. Repeat from step 2 until all the boxes are filled.

Although I know that using this technique, we need to start from the middle of the first row, but due to curiosity, I tried starting from the left corner, right corner, and centre of the second row as well. But this technique does not work for those places. Here are the pictures: 

The technique doesn't work on even number magic squares such as 4 x 4 or 6 x 6 because the square is divided evenly and there is no center for any row or column.

Response on “Was Pythagoras Chinese”

 

Source: https://science.howstuffworks.com/math-concepts/pythagorean-theorem.htm

Does it make a difference to our student’s learning if we acknowledge (or don’t acknowledge) non-European sources of mathematics? Why, or How?

 I think acknowledging non-European sources of mathematics in the classroom will make a difference in students' learning because these sources will help students appreciate other cultures' strengths. They will be able to make connections to their way of doing the math to different methods. It will also build empathy among students and allow them to respect students who use these strategies. To incorporate the non-European way of doing mathematics in the classroom, the teacher should give an inquiry-based research project to students before introducing a new topic. It will allow students to explore the issue before they learn it in the classroom. It will also develop curiosity among them. 

What are your thoughts about the naming of the Pythagorean Theorem, and other named mathematical theorems and concepts (for example, Pascal’s triangle, ……)

 Although naming mathematical formulas and theorems have nothing to do with how they are used, it helps them recognize the person who has created these formulas. Even though I am not against it, I have some confusion about fairness credit given to the founder of the formulas or concepts. Multiple mathematicians founded many theorems, but their credits are only offered to those who have written the solution properly. In my opinion, the acknowledgement should be given to all the mathematicians who have contributed to the answer regardless of the amount of contribution. Furthermore, many mathematicians discovered more than one theorem or formula. If we start naming them all after mathematician's names, it would be hard for them to remember them. It can cause misunderstanding among students. They can easily get confused between different concepts formed by the same mathematicians.

Problem using Egyptian False Position method

Shaan is moving to an apartment with his partner. He wants to spend $ 850 on a dining table with four chairs. If the cost of four chairs is “x” and the cost of a table is $100 more than the cost of a chair, then what will be the cost of chairs and table? (excluding taxes).

Let      

            Cost of four chairs = x

            Cost of a chair = x/4

            Cost of a table = (100 + x/4)

            Total amount = $850

So,

            x + (100 + x/4) = 850

Try  x = 100,    

            100 + 125 = 225 ≠ 850

We need approximately four times the answer to get 850

Now try x = 400

            400 + 200 = 600 ≠ 850

Try x = 600

            600 + 250 = 850

So, the cost of four chairs is $ 600 and the cost of one chair is $150

      The cost of a table is $250.

     

           

 

 

Reflection on Babylonian Word Proble

 

 

After reading, I think that Babylonian word problems are practical because the language in the word problems and the information is given in the word problems were related to their real-life routines such as agriculture, harvesting, or construction of buildings. I believe that pure mathematics and applied mathematics are correlated. We can only use the formulas or given information if that information or formula is proved to be true. I think Babylonian mathematics is pure mathematics to some extent because they used math for their own sake to perform their daily routine work. 

           In terms of generality, I believe that mathematics is all about generalization and abstraction because both are important for understanding the concepts and follow the procedure. The tangible things can turn into abstraction, which helps to generalize the idea of mathematics. Generalization and abstraction help students to understand the concept behind what they are learning. The purpose of a math word problem is to connect us with real life. Everybody uses word problems in their daily routines because it is in our minds all day long. For example: after waking up, we start thinking about how much time I would take to some household work, cleaning, cooking, and go to work.