What would a rectangle even mean on a sphere?
Four right angles.
So it doesn’t fit on a sphere at all?
Good point. Four equal angles, then, although they will each have to be greater than 90 degrees.
I don’t think that would work for just 4 lines? I think you have to have arcs, not straight lines
It’s possible to have an equiangular quadrilateral, i.e. whose sides are geodesics (the analogue of “straight line” on a sphere). The Gauss-Bonnet theorem implies their total interior angle is greater than 2pi, so four right angles can’t work.
Here’s an interactive demo of quadrilaterals on the sphere: https://geogebra.org/m/q83rUj8r
Notice that each side is a segment of a great circle, i.e. a circle that divides the sphere in half. That’s what it means for a path to be a geodesic on the sphere.
many boundary lines “in law” follow longitude/latitude great circles
Copying my reply to someone saying we should change it. Just here to spread the knowledge. :)
"Land surveyor here. That’s actually more complicated than it sounds. You would have to disregard all historical records and section corners throughout the entire state and neighboring states. Section corners are actual physical monuments set in the ground. In the past they’d literally just put a mark on a rock with a chisel. Nowadays we use a rebar with a two inch aluminum cap stuck into the ground similar to the property corners you’d find around your house but bigger. They’re set up in a “grid” all around the state and sections are around 1 square mile with half sections and quarter sections being very common as well.
Whenever someone needs a land surveyor to do anything, the first thing we do is find section corners to orient ourselves because they are known points. We will literally hike miles into the wilderness with field notes from 1892 to go on just to find these things so someone can build a fence. Just because people don’t live there doesn’t mean a section corners doesn’t land in the “grid.” Some of them are so remote it’s a whole day of work just to find one. If these points were to change not only will all of our records from the past 100+ be completely obsolete, we would have to manually set new physical section corners and make a new grid across the entire state. Not only that but all of our information about everything from property lines to the elevation and location of the curb outside your apartment building is all based on those section corners to an extent. The actual legal definition of someone’s property is based on a known section corner with a bearing and distance to the property (Google “land surveying legal description.”). The information for this kinda stuff is like a giant tower of information and records dating back from the 1800’s with everything today being at the top. If you take out the bottom the whole thing collapses. Also we would have to rewrite the legal definition of every single piece of land and property in the entire state if not the country.
Also the funding for it would be astronomical. Like, hundreds of millions of dollars. And most counties are already cutting their land surveyor budgets as we speak."
I hope somebody fixes that. Would be an interesting pledge to run with for governor/president.
Land surveyor here. That’s actually more complicated than it sounds. You would have to disregard all historical records and section corners throughout the entire state and neighboring states. Section corners are actual physical monuments set in the ground. In the past they’d literally just put a mark on a rock with a chisel. Nowadays we use a rebar with a two inch aluminum cap stuck into the ground similar to the property corners you’d find around your house but bigger. They’re set up in a “grid” all around the state and sections are around 1 square mile with half sections and quarter sections being very common as well.
Whenever someone needs a land surveyor to do anything, the first thing we do is find section corners to orient ourselves because they are known points. We will literally hike miles into the wilderness with field notes from 1892 to go on just to find these things so someone can build a fence. Just because people don’t live there doesn’t mean a section corners doesn’t land in the “grid.” Some of them are so remote it’s a whole day of work just to find one. If these points were to change not only will all of our records from the past 100+ be completely obsolete, we would have to manually set new physical section corners and make a new grid across the entire state. Not only that but all of our information about everything from property lines to the elevation and location of the curb outside your apartment building is all based on those section corners to an extent. The actual legal definition of someone’s property is based on a known section corner with a bearing and distance to the property (Google “land surveying legal description.”). The information for this kinda stuff is like a giant tower of information and records dating back from the 1800’s with everything today being at the top. If you take out the bottom the whole thing collapses. Also we would have to rewrite the legal definition of every single piece of land and property in the entire state if not the country.
Also the funding for it would be astronomical. Like, hundreds of millions of dollars. And most counties are already cutting their land surveyor budgets as we speak.
It would be funny to move those slightly.
It’d be funny to move your property corner slightly. It’s basically the same principle. :P
Also it’s a federal crime to fuck with them.
I don’t live there so I don’t mind :)
There are apparently two markers fairly close to where I live so I might check those out someday.
I obviously won’t mess with them though since all crimes are “federal crimes” where I live.
land surveyor vigilantism
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.
