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!
Most of Ancient Egyptian geometry and calculations was relevant to the way their societies were carried out. Geometers, land surveyors, and farmers would have had to work very closely to maximize their resources and best meet the needs of the people. So, in the case of circular area, this would have been important for ensuring efficient farming practices and accountable crop storages. Certainly, the ancient Egyptians would have had a lot more ease in constructing a circular field, where a worker stands in the centre holding one end of a rope, and another worker traces the circumference of the circle to measure out that area.
What's also really cool, is how the Egyptian approximation relates to the Ancient Greek problem of squaring the circle! Squaring the circle is an ancient greek problem, but the Egyptians' formula is a really cool solution to it (this is a great introduction to psuedomathematics)! Even though the phrase 'squaring the circle' today refers to 'attempting the impossible', the Ancient Egyptians got pretty close.
While in my presentation later today I will only briefly touch on the overarching industrial applications, the Egyptians would have had dozens more of uses for the area of a circle, in art, cultural practices, observances of their religious activities, recreation, personal daily use, and low scale agricultural purposes. The circle was pivotal (pun intended), and critical, in efficiently running their societies.
Some references:
https://egypt-tehuti.org/learned-ancient-egyptians/squaring-the-circle/
https://en.wikipedia.org/wiki/Egyptian_geometry
https://gizmodo.com/center-pivot-irrigation-how-to-grow-food-in-the-middle-5811801
https://www.ancient.eu/article/997/ancient-egyptian-agriculture/
Very nice!
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