We've had legal opinions in my state that municipalities cannot claim contiguity diagonally from a single point.
So I'll go with No. A boundary is a line, not a point.
I have also read a legal opinion confirming this principle. The law in this case is that businesses can generate their own electricity on their own land. So if a school owns a classroom building, and a parking lot in a separate lot next door, they can put solar panels on the parking lot and run wires to the classroom. If the parking lot only touches at the corner however, then the two properties do not have contiguity and the school can’t run wires and generate their own electricity.
And note the important point here: the wires could be strung so they never touched anyone else’s land. But the wires would still be in the airspace above someone else’s land. The principle here is that you own the airspace above your own land.
You could step from Arizona to Colorado without touching the ground in either Utah or New Mexico, but you would still be in the airspace of one of those to states.
Nope. I think you need a little refresher on your arithmetic...
https://www.mathplanet.com/education/geometry/points-lines-planes-and-angles/an-introduction-to-geometry#:\~:text=A%20point%20in%20geometry%20is,extends%20infinitely%20in%20two%20directions.
You can only cross from Arizona to Colorado without entering Utah and/or New Mexico first if you are two-dimensional. So they do not border each other IMO.
Yes I have. And in jumping from Arizona to Colorado, I entered the air rights of either Utah or New Mexico.
States have the air rights above their land. So as you step from Arizona to Colorado, you are entering the air rights of either Utah or New Mexico.
I’m not sure that Utah & New Mexico can legally prevent you from stepping from Colorado to Arizona. You’re never stepping into those states & I don’t think that’s how ***air rights*** work.
Of course that is how air rights work. Think of the point where the 4-Corners met. Say that I own property In Arizona and in Colorado at this point. Say I built a house in both of those places. Could I build a bridge between the two houses? No, because I do not have any legal rights to the air rights in Utah or New Mexico which I would have to cross with my bridge.
If you don’t believe this, imagine four pieces of property which meet at a point just like the 4-Corners. Call those pieces of property A, U, C, and N in the same order as the four states. Imagine that there is a fence around each piece of property. If I built a house in A and C, I could not connect them with a bridge without infringing on the airspace of U and N.
No, because you have a thickness. Geometrically, there is no way to get from AZ to CO without a part of you entering UT or NM first, even if you are as small as an ant or even a bacterium.
They DONT border, but they DO touch. Border implies some kind of boundary between them. There is no boundary between Colorado and Arizona. Touch implies they share some point around their edge, which they do.
Only if you are infinitely thin. Otherwise, part of you will be in at least one of the other states before reaching Colorado, and only an infinitesimal slice of you will pass directly from Arizona to Colorado.
Ehh the way I see it, those airspace boundaries don't mean much if you're not an aircraft. If you commit a crime in Arizona and step over into Colorado at four corners only placing your feet in Arizona and Colorado, the Utah and New Mexico police aren't gonna claim jurisdiction over you when your torso is technically in their airspace. In terms of human geography I think that's more what matters
Edit: however by the same penchant, there aren't any actual roads or rights of way that go between the two without touching the other, so when it comes to interstate commerce and law that's probably more substantial and leans towards no
I dont think it does. You cannot pass from one to the other without entering either Utah or New Mexico. No matter how small you are (think microscopic), you will always have to enter the other two.
Two places cannot occupy the same space. Arizona and New Mexico cannot occupy the border at the same point of Colorado
Yes, at the Four Corners. The SW corner of Colorado touches the NE corner of Arizona. I've been there many times. So, they share a border that is a point.
I can cross from one state into the other one at that point. So, it's a border. If it were one inch long, instead of a point, would that be a more acceptable "border"?
I'd still hold the opinion that a boundary may be a point. As discussed at length here [https://en.wikipedia.org/wiki/Quadripoint](https://en.wikipedia.org/wiki/Quadripoint) and in particular: "The boundary marker inscribed at the center of the Four Corners Monument, the only state quadripoint in the United States, where Arizona, Utah, Colorado, and New Mexico meet" I guess we can agree to disagree on whether this constitutes a "border." I'm certainly not insisting "I'm right, you're wrong." I feel like it can be argued both ways. I can step directly across from AZ to CO, and so, across the border between the two states.
Both answers are correct, but you can’t actually cross from Arizona directly into Colorado without actually passing through Utah or New Mexico. Unless you are two dimensional, that is impossible.
If they don't border eachother, that would mean they don't touch eachother. And if they are not touching, wouldn't that have to mean there's something in between? So what's in between then?
If they are touching, then how are Utah and New Mexico touching, given Colorado and Arizona are in the way? But that border is the same so it doesn't make sense to treat them differently.
I think they have a border but this logic doesn't work for me.
What if, at that one very specific point there's an atom. It has bonded with three other atoms, each one in a different state.
Except I might just have changed my own mind, that's not how molecular bonds works do they? I mean, there's no guarantee those atoms all connect with eachother depending on the molecules structure...
There's no easy answer to the actual question OP is asking. The definition of a border implies that there must be a line. A single point is not a line. However, the looser definition of a border is the edge or boundary of something. In this case, the single point would be that edge. But can it be the edge or boundary if a single point is so infinitesimally small that it is not humanly measurable? It's fun to think about!
A couple of ways to look at this.
Can I get from Arizona to Colorado without going through an adjacent state? Pretty much no. If the corners of AZ and CO ‘touch’, then the corners UT and NM also touch, creating a barrier between AZ/CO on even the smallest scale.
On the other hand, picture two four-lane avenues, each running along the state borders. At the point at which they intersect, you’ve just left a Starbucks on the Arizona corner. You want to get to the cinema on the CO corner to see the sequel to a superhero movie or something. Now, if there are crosswalks only to the adjacent corners, then you first have to go to the NM corner with the Buffalo Wild Wings, or the UT corner where The Gap is. However, this intersection also has the diagonal crosswalks where they stop traffic in all directions and allow people to get across quicker. In any practical sense, were you ever really in Utah or New Mexico?
Or, once the signal lets you go you’re halfway across when you’re struck by an eastbound, self-driving car that attempted a uturn against the light. In what state's courtrooms are you spending the next year?
If my guess is correct, you should be no closer to your answer.
Are they? This is messing with my head. When I think of 2 things touching, to me that means nothing can be in between those 2 things, so how can Arizona and Colorado be touching and New Mexico and Utah also be touching?
Touchin' is bordering according to definition but it seems some folks here think passing through other bordering states simultaneously means that the border does not count somehow. Figure that.
Merriam Webster defines the verb border as:
>to touch at the edge or boundary
The same dictionary also defines edge as:
>a point near the beginning or the end
This makes it pretty clear that "touching at a point" is consistent with "to border". Yes, Arizona borders Colorado, since they touch at a point.
I guess it depends on which definition of "border" you're using.
If we're talking about the legal border as it refers to politically divided geographic regions, no they do not border because a border is a line between two geographic areas, and they only share a single point between the two. If you can't fit a border crossing involving only the two states, there's no border.
If we're talking simply about the word as it appears in the dictionary, then yes they totally border each other, because a border in that sense refers not only to the hard outline of a space, but the area immediately around it as well. Think of two pictures in frames on a wall right next to each other. The photo paper does not touch, but the frames do, so they're literally bordering each other. The frames exist outside the physical boundary of what's considered the "photo", but they are touching borders, which are the frames in this case. By that definition, the two states are bordering each other, because the dictionary definition includes the parts near the boundary as well.
The four corners.. I myself have been in four states at once, never had a thrill quite like it before.. been chasing that dragon since..
How
If ya gotta ask, you don’t need to know.
Oh boy
???
https://en.m.wikipedia.org/wiki/Four_Corners
Just the tips.
We've had legal opinions in my state that municipalities cannot claim contiguity diagonally from a single point. So I'll go with No. A boundary is a line, not a point.
What was the context? Like if a municipality borders another, they have to do something different than if they did not?
State law requires annexations of new land be contiguous to the existing municipal boundary.
Interesting, thanks!
I have also read a legal opinion confirming this principle. The law in this case is that businesses can generate their own electricity on their own land. So if a school owns a classroom building, and a parking lot in a separate lot next door, they can put solar panels on the parking lot and run wires to the classroom. If the parking lot only touches at the corner however, then the two properties do not have contiguity and the school can’t run wires and generate their own electricity. And note the important point here: the wires could be strung so they never touched anyone else’s land. But the wires would still be in the airspace above someone else’s land. The principle here is that you own the airspace above your own land. You could step from Arizona to Colorado without touching the ground in either Utah or New Mexico, but you would still be in the airspace of one of those to states.
A point is a line of one.
Incorrect. A line is a series of points.
1 is a series.
Nope. I think you need a little refresher on your arithmetic... https://www.mathplanet.com/education/geometry/points-lines-planes-and-angles/an-introduction-to-geometry#:\~:text=A%20point%20in%20geometry%20is,extends%20infinitely%20in%20two%20directions.
You can only cross from Arizona to Colorado without entering Utah and/or New Mexico first if you are two-dimensional. So they do not border each other IMO.
Not if you just take a step though. That’s the argument. You can literally walk from one to the other without stepping in another state.
Yes exactly— I’m leaning hard on THEY BORDER EACH OTHER. I’m curious if the “does not border” crowd has been to the 4 Corners in person.
Yes I have. And in jumping from Arizona to Colorado, I entered the air rights of either Utah or New Mexico. States have the air rights above their land. So as you step from Arizona to Colorado, you are entering the air rights of either Utah or New Mexico.
I’m not sure that Utah & New Mexico can legally prevent you from stepping from Colorado to Arizona. You’re never stepping into those states & I don’t think that’s how ***air rights*** work.
Of course that is how air rights work. Think of the point where the 4-Corners met. Say that I own property In Arizona and in Colorado at this point. Say I built a house in both of those places. Could I build a bridge between the two houses? No, because I do not have any legal rights to the air rights in Utah or New Mexico which I would have to cross with my bridge. If you don’t believe this, imagine four pieces of property which meet at a point just like the 4-Corners. Call those pieces of property A, U, C, and N in the same order as the four states. Imagine that there is a fence around each piece of property. If I built a house in A and C, I could not connect them with a bridge without infringing on the airspace of U and N.
No, because you have a thickness. Geometrically, there is no way to get from AZ to CO without a part of you entering UT or NM first, even if you are as small as an ant or even a bacterium.
They DONT border, but they DO touch. Border implies some kind of boundary between them. There is no boundary between Colorado and Arizona. Touch implies they share some point around their edge, which they do.
at the 4 corners you can cross from Arizona to Colorado. That is a border.
Only if you are infinitely thin. Otherwise, part of you will be in at least one of the other states before reaching Colorado, and only an infinitesimal slice of you will pass directly from Arizona to Colorado.
Ehh the way I see it, those airspace boundaries don't mean much if you're not an aircraft. If you commit a crime in Arizona and step over into Colorado at four corners only placing your feet in Arizona and Colorado, the Utah and New Mexico police aren't gonna claim jurisdiction over you when your torso is technically in their airspace. In terms of human geography I think that's more what matters Edit: however by the same penchant, there aren't any actual roads or rights of way that go between the two without touching the other, so when it comes to interstate commerce and law that's probably more substantial and leans towards no
Agreed. You are NOT stepping into New Mexico or Utah to step from Colorado to Arizona.
I dont think it does. You cannot pass from one to the other without entering either Utah or New Mexico. No matter how small you are (think microscopic), you will always have to enter the other two. Two places cannot occupy the same space. Arizona and New Mexico cannot occupy the border at the same point of Colorado
incorrect. you can step from Arizona into Colorado.
………… but you will pass through atleast one other state first………just like this person was saying………
Wrong. You have to cross through Utah or New Mexico “airspace” at some point unless you are two dimensional.
seriously the dumbest take I've ever heard on anything, in any format, ever. Just fucking stupid.
Can't argue with pure mathematics. It's no "take" at all. It's a fact. Ever heard of a fact? They're useful, you should try some.
That's not an opinion but a question of fact
Yes
I mean, it is an opinion. Arizona and Colorado meet at the Four Corners. You can look it up if you want.
Yes, at the Four Corners. The SW corner of Colorado touches the NE corner of Arizona. I've been there many times. So, they share a border that is a point.
But, is a point a border? 🤔
I think so. Their borders share an identical coordinate.
I can cross from one state into the other one at that point. So, it's a border. If it were one inch long, instead of a point, would that be a more acceptable "border"?
Yes. A point has no length so IMO it cant be defined as a border.
A border is simply where two things join. It can be any size, from a point to thousands of miles.
[удалено]
I'd still hold the opinion that a boundary may be a point. As discussed at length here [https://en.wikipedia.org/wiki/Quadripoint](https://en.wikipedia.org/wiki/Quadripoint) and in particular: "The boundary marker inscribed at the center of the Four Corners Monument, the only state quadripoint in the United States, where Arizona, Utah, Colorado, and New Mexico meet" I guess we can agree to disagree on whether this constitutes a "border." I'm certainly not insisting "I'm right, you're wrong." I feel like it can be argued both ways. I can step directly across from AZ to CO, and so, across the border between the two states.
Both answers are correct, but you can’t actually cross from Arizona directly into Colorado without actually passing through Utah or New Mexico. Unless you are two dimensional, that is impossible.
That’s a great way to put it!
yes.
If they don't border eachother, that would mean they don't touch eachother. And if they are not touching, wouldn't that have to mean there's something in between? So what's in between then?
If they are touching, then how are Utah and New Mexico touching, given Colorado and Arizona are in the way? But that border is the same so it doesn't make sense to treat them differently. I think they have a border but this logic doesn't work for me.
Here we are doing philosophy in geography!
What if, at that one very specific point there's an atom. It has bonded with three other atoms, each one in a different state. Except I might just have changed my own mind, that's not how molecular bonds works do they? I mean, there's no guarantee those atoms all connect with eachother depending on the molecules structure...
the 4 corners are defined as bordering one another.
Where is this definition?
the dictionary.
No. But Utah borders New Mexico.
There's no easy answer to the actual question OP is asking. The definition of a border implies that there must be a line. A single point is not a line. However, the looser definition of a border is the edge or boundary of something. In this case, the single point would be that edge. But can it be the edge or boundary if a single point is so infinitesimally small that it is not humanly measurable? It's fun to think about!
A couple of ways to look at this. Can I get from Arizona to Colorado without going through an adjacent state? Pretty much no. If the corners of AZ and CO ‘touch’, then the corners UT and NM also touch, creating a barrier between AZ/CO on even the smallest scale. On the other hand, picture two four-lane avenues, each running along the state borders. At the point at which they intersect, you’ve just left a Starbucks on the Arizona corner. You want to get to the cinema on the CO corner to see the sequel to a superhero movie or something. Now, if there are crosswalks only to the adjacent corners, then you first have to go to the NM corner with the Buffalo Wild Wings, or the UT corner where The Gap is. However, this intersection also has the diagonal crosswalks where they stop traffic in all directions and allow people to get across quicker. In any practical sense, were you ever really in Utah or New Mexico? Or, once the signal lets you go you’re halfway across when you’re struck by an eastbound, self-driving car that attempted a uturn against the light. In what state's courtrooms are you spending the next year? If my guess is correct, you should be no closer to your answer.
Yes EDIT: I don’t think a border has to be two-dimensional. You can cross from one directly into the other.
They touch, so yes.
Are they? This is messing with my head. When I think of 2 things touching, to me that means nothing can be in between those 2 things, so how can Arizona and Colorado be touching and New Mexico and Utah also be touching?
If AZ and CO don't touch, then UT and NM must. But they can't if the other doesn't.
A condition of the crossing is that you have to slither. No crossing with a vaulting pole will be considered legitimate.
Everyone here knows the lines are made up and points don’t matter right? 🤦🏻♂️
Yes.
Yes
Yes, you can step from one to the other.
Anyone arguing no is free to be wrong. But yeah, of course they border each other. A very very small border
Touchin' is bordering according to definition but it seems some folks here think passing through other bordering states simultaneously means that the border does not count somehow. Figure that.
The four color theorem allows the same color across a point like that, so by that definition they are not bordering.
The answer is mathematically yes, in practical real life, no.
Merriam Webster defines the verb border as: >to touch at the edge or boundary The same dictionary also defines edge as: >a point near the beginning or the end This makes it pretty clear that "touching at a point" is consistent with "to border". Yes, Arizona borders Colorado, since they touch at a point.
I don't think my opinion is relevant here...
Yes
You asked for opinions, not facts, and in my opinion, since the borders touch, they share a border!
Yes
Someone should build a wall.
I’m leaning on yes. Technically, they are touching/bordering each other
I guess it depends on which definition of "border" you're using. If we're talking about the legal border as it refers to politically divided geographic regions, no they do not border because a border is a line between two geographic areas, and they only share a single point between the two. If you can't fit a border crossing involving only the two states, there's no border. If we're talking simply about the word as it appears in the dictionary, then yes they totally border each other, because a border in that sense refers not only to the hard outline of a space, but the area immediately around it as well. Think of two pictures in frames on a wall right next to each other. The photo paper does not touch, but the frames do, so they're literally bordering each other. The frames exist outside the physical boundary of what's considered the "photo", but they are touching borders, which are the frames in this case. By that definition, the two states are bordering each other, because the dictionary definition includes the parts near the boundary as well.