Eye of Horus, Unit fractions in Ancient Egypt, and Special Numbers!

Research on the significance of the Eye of Horus:

The Eye of Horus is a very packed symbol! Not only did each of the fractions 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64 have denominators comprised of the first 6 powers of 2, they also represented Heqat fractions, which was an Egyptian measuring unit for grains and flour, and each of the fractions accounted for a different human sense. 1/2 accounted for the sense of smell, 1/4 for sight, 1/8 for thought, 1/16 for hearing, 1/32 for taste, and 1/64 for touch. I'm a bit curious as to why the fractions were allocated towards each sense as such; I would have expected that 'thought' would be paired with the largest fraction, 1/2, since it's deemed as the most important sense. One of the articles I read presented an insightful explanation as to why which fractions were paired with what sense, however, they concluded that their explanation was mere speculation that took Egyptian mastery of medicine, arts, and mysticism into consideration. After studying the Babylonian base 60 system, I find it really interesting that the Egyptians had a particular affinity to base 2. I'm surprised that the Heqat fractions didn't include 1/3 or 1/5, which I think would have been more practical as a measuring unit for grains and flour, than 1/32 or 1/64. However, I imagine that based on real-life situations of providing grains and flour for Egyptian communities, it might have been more convenient to have a base 2 system for rationing portions.

Constructing a Magic Square

I chose to try a 4x4 magic square, as I had already worked on a 3x3 previously. Since the side length of the square was 4 and the area was 16 (or 4 squared), in order to be nerdy and consistent I made the target sum 64 (or 4 cubed). Take a look at the picture below for the solution and the variable placements that I refer to throughout this post. 

Egyptian Algebra: 'Method of False Position'

Here is my sample word problem:

By 2050, it is estimated that there will be a one-third decline in the polar bear population. If there are 16000 polar bears left, how many were there to start with?

Modern Method:

16000 = x - x/3

48000 = 2x

24000 = x

“Was Pythagorus Chinese” Reflections

I’ve honestly never thought about this before! I’ve always taken for granted that Pythagorus was Greek, especially since the graphics in classroom posters always depicted him as such, and this reflects the strong Western-Eurocentric influence on our learning. 

I feel the need to refresh and reconstruct my understanding of so many mathematical ideas that have been presented in my classes over the years. I had no idea that in other parts of the world, even today, that the Pythagorean Theorem is known as the Gougu Rule. And, I definitely did not know that Pascal's Triangle, which was invented in 11th century by mathematician Jia Xian, was re-invented by Blaise Pascal in the 17th century, and that's the version that we are taught today. (This brings me back to another class, where we were shown that Avicenna and Averroes, two polymaths mostly recognized for their contributions to philosophy, are actually Ibn Sina and Ibn Rushd, respectively.) It seems that Eurocentrism permeates our education much more than we are able to understand at surface level, and I don't think that's right.

“A man left Albuquerque heading East” Babylonian Word Problems Reflections

Like most math students out there, I’ve got a love-hate relationship with word problems. Word problems are a great way to solidify concepts and they encourage students to think outside the box for solutions. However, the practicality and importance of word problems are often undermined due to occasionally wacky or excessively difficult examples that overwhelm and confuse students. More often than not, that inability to consistently connect their math work to their life is what affects today’s students the most. 

Assignment 1: Egyptian Approximation to the Circle

Please refer to Kelsea's blog for the solution to Problem 1.2.1, and to Zach's blog for the problem extension.

Below, I’ve outlined a brief summary of my presentation to the background of the problem.

The ancient Egyptians had an incredibly optimal location, along the Nile River, that contributed to their thriving success as a nation. The Nile provided them with clean, fertile water that was used for both personal and industrial purposes, such as for transportation, drinking, sanitization, and agriculture. This allowed them to successfully carry out large scale agricultural practices to suit the needs of their growing population. In addition, this was especially important because they could grow both staple food and trade crops, such as barley, wheat, and the papyrus, on which they wrote!