Interesting Findings of The Eye of Horus

The Eye of Horus, also called “Wedjat”, is an ancient symbol which represents protection, health, and rejuvenation, according to Ancient Origins.  In ancient Egyptian myth, Horus was the sky god.  His right eye was associated with the sun god Ra and his left eye was associated with the moon god Djehuti.  One version explained that Horus lost his left eye in the battle with his uncle, while another version said that “he gouged his eye out as a sacrifice to bring his father back from the dead” (Dhwty, 2018).   In both cases, Horus was able to restore his eye magically.  In ancient Egypt, people usually used Eye of Horus as funerary amulet.  Even today, many Mediterranean fishermen still paint it on their fishing boats for protection.

Not only the myth behind the Eye of Horus was fascination, its mathematical implications associated with Egyptian’s unit fraction and different senses are interesting.  In ancient Egypt, fractions were written in the format of unit fraction.  It is believed that the 6 parts of the Horus’ left eye represent different unit fraction:

the right side of the eye = ½                      associated with sense of smell

the pupil = ¼                                              associated with sight

the eyebrow = 1/8                                      represents thought

the left side of the eye = 1/16                    represents hearing

the curved tail = 1/32                                 represents food

the teardrop = 1/64                                     represents sense of touch

However, this theory has been proved to be incorrect in the 1970s.  Another interesting thing was that Egyptian unit fraction can be convenient when dividing items into equal shares.

Are there examples in your life or in the life of those around you of numbers that have special meanings or are connected to stories?

For Chinese, numbers are often associated with luck, health, fortune etc.  For example, number 5 represents a good luck, 6 represents a smooth life, 8 represents having lots of money.  On the other hand, 7 means angry,18 represents the hell.  These representations came from superstitious beliefs from the old days and were honored by the older generations.  The pronunciation of these numbers often associate with Chinese characters which have the above meanings.  In addition, many Chinese also link their birth dates to fortune.  For example, if a boy was born on a date associated with number 5, 2 or 8, and a girl was born on a date associated with numbers of 3,6, and 9, then they are considered to be lucky persons and will have very healthy and wealthy lives.  I guess that was one of the reasons for me to marry my husband who was born on a date with all the lucky numbers.  It proved to be false!!! (Just joking!)

Reference

Dhwty. (2018). Eye of Horus: The True Meaning of an Ancient, Powerful Symbol. Ancient

Origins. Retrieved from

https://www.ancient-origins.net/artifacts-other-artifacts/eye-horus-0011014

Magic Square

I didn't realize that this question was the one mentioned in one of the most famous Chinese Wuxia novel until later on. This question was called "Jiu Gong Ge", meaning there are 9 squares.  It was my favorite novel written by Yong Jin and it was my childhood memory! 

When I first thought about how to solve this problem, I didn't have any clue. I just put the numbers randomly into the square boxes and see if they would add up to 15. It didn't work. 

Then I knew I needed to find the middle number in order to solve the problem. I started to look for all possible combinations of 3 numbers which add up to be 15. I found out that 5 must be the number in the middle since it is the only one number when adding together with other two different numbers equals 15 but also include the rest of the 8 numbers. 

Once I found 5 as the middle number, I figured out how the combinations of the 8 numbers which add up equals 15. Finally just put the numbers into the square boxes and make sure the row, columns and diagonals add together all equal 15.

My ugly trial and error worksheets:

 

The Method of “False Position”

Problem: Kristina has a quantity of toys. The quantity and its 1/8 added together equals the total number of Mia's toys, which is 18. How many toys does Kristina have?

Assume the quantity is 8:

1                                      8

1/8                   1

Total                9

As many times as 9 must be multiplied to get 18, so many times 8 must be multiplied to give the required number. Multiply 9 to get 18:

1                                      9

2                                    18

                                    Total    2

Multiply 2 by 8 to get

1                                       2

2                                       4

4.                        8           

8                     16

The quantity is                                             16

                                                1/8                   2

                                                Total               18

Therefore, Kristina has 16 toys in total.

 

Was Pythagoras Chinese? - To Revisit the Ancient Chinese’s Contribution in Mathematics

 

As the author mentioned in the end of the article, due to geographic isolation, Chinese scholars’ work and their contribution in mathematics has been ignored for centuries.  It worth our efforts to recognize and give credits for their brilliant and astounding discovery.  I do see the value of acknowledging the non-European source of mathematics in our students’ learning.  By doing so, our students will not only grasp the mathematical concepts we convey, but also will have a comparable knowledge in terms of where the mathematical theory comes from.  I think who was the real inventor of a certain mathematical theorem is not the point for us to introduce non-European source of mathematics, our focus should be how to shape our students’ perspectives and to have a holistic point of view on every subject they encounter, it could be math, history, or any other subjects.  That is the ideal model of democratic education, which is to create independent and critical thinkers.   

I have done some research in one of my previous blog posts about the naming of Pythagorean Theorem.  I learned that although the theorem was named after him, Pythagoras was actually not famous for his mathematical contribution, rather for his expertise on the fate of the soul after death and religious ritual.  There was no formal record that accounted he was the actual creator of Pythagoras Theorem, according to Stanford Encyclopedia.  To my amazement, once again, I found that before Pascal’s time, there were several scholars have discovered the secret of triangular array or binomial coefficients.  It was Pascal who innovated these previous unattested uses of the numbers and offered a systemic study on this subject.  The same mathematical concept was studied by Chinese mathematician Jia Xian and presented by Yang Hui in the 13^th century as well, and it was named as Yang Hui’s Triangle.  No matter which mathematician took the credit for a certain mathematical discovery, it reflects our ancestors diligent work in progressing and developing the subject of mathematics. We should be acknowledged and be appreciative for all their contribution in our human advancement.

442 Presentation- 10.04 by ivy on Scribd

 

The Idea of Pure and Practical Mathematics

Oftentimes we as mathematicians, math teachers and anyone else who enjoys mathematics clearly see the practicality in studying such an abstract language.  I believe that many teachers use word problems in attempt to share and show students their love for mathematics, hoping they can later on transform those abstract mathematical concepts to a more practical use.  For example, rther than teaching the very dry concepts of sine, cosine and tangent, it could be more exciting to link it to the ancient Greek problem of bow hunting.  The idea of sine came from the Greek problem of a bow string at rest versus when it was stretched is interesting.  We then can connect this idea to the common representation of opposite over hypotenuse or y value over the radius. Was this invention a simple practical daily use or for the Greek to advance their pure scientific study such as astronomy?  Likewise, the ancient Babylonian mathematics which has the impression of “merely practical” at the beginning, but the structure of the unknowns is far from practical. Then how can we draw conclusion on which school does Babylonian mathematics belong to, pure or applied?  Therefore, I agree with Robson’s argument that we truly cannot separate math into a dichotomy between “pure” and “applied or practical”.