A "you" can, and many individual "you"s presumably did that, to general satisfaction. But the implicit assumption you made is that eyeballing and cutting is easy, while triangles are hard, even though it's the other way around, especially with stone age tools.

But we're talking about groups of people, "they", who all build a lot. Such groups tend to have a few people who make these observations, and then the observations proliferate, because they are both way easier to use than the alternative hack-work, and yield much more aesthetically pleasing results. Especially in the stone age when you nornally don't have easy access to anything at all with a right angle (unlike in modern construction) and you build stuff out of clay bricks, where minor inaccuracies inevitably add up and make your life much harder down the road. Tying together three pieces of string with prescribed ratios, pull it tight was a very easy way to get a right angle compared to anything that came before.

It's necessary in the sense that stone age construction is so much easier if you know about it, and so much harder if you don't. Those who didn't come up with it didn't do such construction, because doing difficult things is harder than doing easy things.

You can easily accurately lay out a large square without knowledge of Pythagorean Theorem.

1. lay out a straight line 2x in length.

2. find midpoint (easy by drawing an arc with a string from each end point. Basic compass & ruler technique.

3. draw another arc from the midpoint, of radius 1x. Try different spots on the arc until it is equidistant from each of the endpoints of the line.

4. voila! an accurate right angle. Laying out the rest of the square is now trivial.

>A "you" can, and many individual "you"s presumably did that, to general satisfaction

I was chatting with the person that was in charge of marking the fields for the local youth soccer league. I volunteered to help one weekend, and one of the first things he asked was if I knew what a 3/4/5 triangle was since it was the only way to know you'll be squared. I never did figure out to what level he was dead panning his joke or if he was even meaning for it to be a joke. Either way, I laughed.

3/4/5 is considered a wood working trick - that many beginners would not know (according to youtube, at least)

I learned it in geometry in like 10th grade. No wood involved.

I think you mean bronze age.

I don't think I do. I'm fairly confident that the people of the chalcolithic did enough large scale construction (and pottery and watching the night skies and so on) to have figured a whole lot of empirically accessible geometry out.

The _article_ happens to be about written sources from the Bronze Age Babylonians, which lets us glimpse at their accumulated knowledge. But there's no reason to believe this knowledge was particularly new at their time, and this was a clay tablet equivalent of an arXiv preprint.

I built a tree house for my kids. I didn't exactly eyeball it but my amateur technique and planning left me having to do a lot of compensation for things being out of square.

Everything becomes a custom cut, often in multiple dimensions and all earlier errors cascade all the way to the end.

> Everything becomes a custom cut, often in multiple dimensions and all earlier errors cascade all the way to the end.

Unrelated, but that sounds exactly like many software projects I've been unfortunately part of.

> I don't see why that was necessary. You can get pretty far with eyeballing it and custom cutting to fit.

i'm not saying at all that I know the answer, but eyeballing and cutting is good for a patio, but on a ziggurat or pyramid scale it seems you don't do so much eyeballing or cutting, and more planning how much material and how many slaves you're going to need for how long, and where to put the doors so the passageways will meet up, that sort of thing.

Please, stop this slave nonsense. Pyramids were built by highly skilled workers, it was prestigious job.

I remember reading about the worker homes and tombs, and I know that skeletal records also showed the workers had much muscular strain. So, it's impossible to deny that there were skilled laborers working on the pyramids, but just because some of the laborers were proven to be skilled and not slaves, doesn't mean slaves weren't used.

The scale doesn't seem right to me. I still can't fathom how that much could be done without using slave labor. If I remember correctly, they layed a block like every 6 minutes for 20+ years.

Do you know how many tombs of laborers were found, or where I could find more aobut that information? I'm very novice when it comes to Egypt

I've seen many Mayan structures in Mexico, and they all look like they were eyeballed.

I'm currently in a brick build house which has a good ten percent slope, because the earth sank, but it hasn't collapsed. I'm pretty sure its not older than a hundred years and I'm amazed it still stands because it sure wasn't designed like this.

Ancient Mesopotamian laws sometimes flayed people alive for incompetent or corrupt work. Those types of mild punishments are good incentive to use the right angles. Pun intended.

Money works a lot better than flogging.