Results 1 to 9 of 9
Like Tree1Thanks
  • 1 Post By skeeter

Thread: Do corners touch?

  1. #1
    Newbie
    Joined
    Jan 2017
    From
    CA
    Posts
    2

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,443
    Thanks
    272

    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?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,680
    Thanks
    2643

    Re: Do corners touch?

    Quote Originally Posted by DanoMan View Post
    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,249
    Thanks
    2233

    Re: Do corners touch?

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

    where on Earth did you come up with that one?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    15,400
    Thanks
    3341

    Re: Do corners touch?

    Quote Originally Posted by romsek View Post
    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 ...
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,443
    Thanks
    272

    Re: Do corners touch?

    Romsek: "where on Earth did you come up with that one?"
    Answer: East end of Ottawa, Ontario, Canada

    Skeeter: "knowing Denis, it probably was an epiphany inspired
    by mass consumption of Labatt's Blue ... "
    Answer: close...Labatt's 50
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jan 2017
    From
    CA
    Posts
    2

    Re: Do corners touch?

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

    Quote Originally Posted by HallsofIvy View Post
    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:

    https://www.youtube.com/watch?v=WlcXoz6tn4g
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,680
    Thanks
    2643

    Re: Do corners touch?

    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?
    0. That's pretty definite!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,970
    Thanks
    665
    Awards
    1

    Re: Do corners touch?

    I think we've addressed all the relevant issues here.

    Thread closed.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: May 28th 2013, 01:02 PM
  2. Replies: 13
    Last Post: Aug 11th 2012, 11:02 PM
  3. Corners of a Cube
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Aug 16th 2009, 02:26 AM
  4. Do The "Four Corners" States Actually touch?
    Posted in the Geometry Forum
    Replies: 3
    Last Post: May 9th 2009, 08:00 AM

/mathhelpforum @mathhelpforum