One thing that was surprising to learn (from our discussion in class) was learning about the way builders and construction workers make 90 degrees, was by 3 4 5, mostly passed down from word of mouth from experienced coworkers, who also attained the information in that way. They learn math through a practical lens, as opposed to the way we do in schools. Egyptians used the plumb bobs (I had to look up what that was), was created to establish the line straight down. The process of using tools that are readily available to create mathematical ideas in practice seems to be a common theme.
What was not so surprising to learn was that geometry emerged, largely out of need for building complex constructions and to implement taxation. It reminds me that we are much of the same people as we were thousands of years ago, and that societal needs like shelter and governance were present for much of our history.
Another thing I was curious about was whether they verified their methods, and how accurate it could be. The question of whether small errors here and there would add up to break a system is interesting. I can think that in our current time, we take pennies out of circulation and they are thinking about taking the nickel out, and I remember seeing that it has no significant effect. I wonder if much of their inaccuracies worked the same way.
You connected practical knowledge like the 3-4-5 triangle and plumb bobs with broader themes of how math emerges from daily needs, and you raised an interesting question about the accumulation of small errors. It shows a thoughtful balance between historical context and present-day parallels.
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