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TIL Colorado isn’t a rectangle and actually has 697 sides, mostly due to poor measurement tools
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Are the section corners' gps coordinates not recorded?
These days we can. We use GPS that's accurate within about a hundredth to a thousandth of a foot. These days we can get a basic idea where it is within a hundred feet or so, but we still have to go find the point to make sure it's even there. We can't just assume it's where it says it is based on old records from before GPS even existed. So we have to go find it. And the thing is that if you find a section corner and find that it's off by 15 feet to the east, you don't set a new section corner because that specific point is the section corner. And everything from property lines and roads to the dimensions of every building in the area are based on where that section corner is, not where it should be. We're talking property lines that were laid out a hundred years ago. And the GPS we use for things like Google Maps is not even close to accurate enough, so we can't use that as a base either.
It can get way more complicated than that. I won't go into too much detail, but it could be something small like the fact that states are divided into different "planes" because the Earth is round and inconsistent, to the actual movement of tectonic plates. Like, if you incorrectly choose the wrong state plane for GPS you could find yourself literal miles from where it actually is.