1. ## Do corners touch?

I'm following a debate on a YouTube video regarding corners of shapes touching. It's about whether the four US states that meet at four corners monument actually all touch one another.

One poster says that they do. The other poster says that they meet, yet don't touch because a point has an infinitesimally small area, that no actual border really exists.

Looking for the truth of the matter. Thanks.

2. ## Re: Do corners touch?

Huh? What's the word "monument" doing there?

Well, when 2 lines intersect, the 4 angles formed = 360 degrees:
so they must touch...don't matter if they're States lines or not...

I believe Saint Motorcai is the patron saint for crossing state lines:
perhaps you could pray to him for inspiration?

3. ## Re: Do corners touch?

Originally Posted by DanoMan
I'm following a debate on a YouTube video regarding corners of shapes touching. It's about whether the four US states that meet at four corners monument actually all touch one another.

One poster says that they do. The other poster says that they meet, yet don't touch because a point has an infinitesimally small area, that no actual border really exists.

Looking for the truth of the matter. Thanks.
This what happens when you don't define your terms!
You can't do this as "Euclidean geometry" because "touch" is not defined in "Euclidean geometry" so you can say either that "it touches" or "it doesn't" depending on how you define "touch"!

As for "no actual border really exists", what definition of "border" are you using? Why can't a single point be a border?

4. ## Re: Do corners touch?

Originally Posted by DenisB
I believe Saint Motorcai is the patron saint for crossing state lines <snip>

where on Earth did you come up with that one?

5. ## Re: Do corners touch?

Originally Posted by romsek
where on Earth did you come up with that one?
knowing Denis, it probably was an epiphany inspired by mass consumption of Labatt's Blue ...

6. ## Re: Do corners touch?

Romsek: "where on Earth did you come up with that one?"

Skeeter: "knowing Denis, it probably was an epiphany inspired
by mass consumption of Labatt's Blue ... "

7. ## Re: Do corners touch?

Originally Posted by DenisB
Huh? What's the word "monument" doing there?
https://en.wikipedia.org/wiki/Four_Corners_Monument

Originally Posted by HallsofIvy
This what happens when you don't define your terms!
You can't do this as "Euclidean geometry" because "touch" is not defined in "Euclidean geometry" so you can say either that "it touches" or "it doesn't" depending on how you define "touch"!
Actually, one of the two posters was asked this multiple times and didn't answer.

As for "no actual border really exists", what definition of "border" are you using? Why can't a single point be a border?
As I said in my post, it wasn't me making that claim. But one reason that I can think of is that a border between two states has a definite length. What is the length of a point?

Anyway, the argument can be found here: