Response to "Mathematics in ancient Egypt"

From the article, it confirmed the in-class discussions we had on the mural, which I appreciate. The mural depicts ancient Egyptian surveyors measuring agricultural land, most likely for the purposes of fair distribution after the annual floods. The article also discusses the many units of length, and how angles were measured.

My questions correspond to these units of length, and the methods of constructing angles. The first oddity that I thought about was related to the differences between the "royal cubit" and the "short cubit". It made sense to me that the ancient Egyptians couldn't settle on a formal definition considering that it took forever for places like Europe as well, but the article seems to default to the royal definition of 7 palms and 28 fingers, never mentioning short cubits again (perhaps for the purpose of simplifying cubits to the reader). Another strange thing about the topic of cubits is that it was considered "the length from the elbow to the tip of the middle finger". I asked myself, "Who was the standard reference for the exact length of a cubit?" This is further mystified by the article's wording; it simply says "most often about 524 mm" instead of something more concrete. Although not the same, it feels like it has tie-ins with the imperial measurement system where units are named after tangible objects such as yards and feet. ("What do you mean my foot isn't 12 inches long? Is anyone's foot 12 inches long?" I would ask as a child.) 

The most surprising part is that despite all these inconsistencies and seemingly arbitrary details, there are genuinely beautiful results that come from the cubit, such as the remen and its properties. The remen was a unit of length that was half the diagonal of a square royal cubit. Having a square of length 1 cubit, it has 2 times the area of a square of length 1 remen and 1/2 the area of a square of length 2 remens, and all of this seems too good to be true, especially since the cubit's length is stemmed from a seemingly random ancient Egyptian's bodily parts and no one could really settle on its actual length.

The other source of confusion I initially had was with the section on constructing right angles. Right angles seemed to me like they should be easy to construct, but this is also coming from someone who has never needed to measure or survey large areas and lengths. That being said, my question was, "Is it that hard to construct right angles, even if the distances are that large?" I was reading the article and they gave explanations involving all this equipment and equilateral triangle and rhomboid strategies, and thought, "If I just showed them what a right triangle is, why can't they just mark a perpendicular line off whatever base line they are going off of?" I could see different angles needing different techniques, but a right angle doesn't seem like the hardest thing to create accurately as long as we keep our ropes straight and angle maintained at the intersection point of the two perpendicular lines. I can see the plumb bobs being useful if we had to construct a right angle vertically, but with a flat plane it just seems excessively elaborate. One reason for all these elaborate methods that I could think of is this: they may also need to verify if an angle is right or not. Maybe the ancient Egyptians got interrupted during angle construction and they had to revisit their measurements, in which case these elaborate methods would be worth it.