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Math Help - Do The "Four Corners" States Actually touch?

  1. #1
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    Do The "Four Corners" States Actually touch?

    I was asked this question in another forum & my answer was that none of them actually touch, they merely share the same intersect point, however small:
    Do the corners of Arizona and Colorado touch each other?

    If Yes, then Do the corners of New Mexico and Utah touch each other?

    If Yes, then How can the corners of Arizona and Colorado touch each other?
    I tried to use the following graphic to illustrate my point that they are not two lines but four "squares" whose corners meet at the coordinate 0,0 on a basic graph.



    Does anyone have a more logical explanation or am I completely off base?

    I really appreciate any & all help.
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  2. #2
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    Hello, ThrowCop!

    If your definition of "two regions touch each other" is something like:
    . . "Uh, like, it's when two regions are sort of ... kind of ...
    . . um ... y'know ... next to each other ... know wot I mean?"
    then we have no basis for any conversation.

    If your definition is: "the two regions share at least one common point",
    . . then we must agree that all four states "touch each other."

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  3. #3
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    Thanks for the reply. That was my answer as well but I could not convince others that the four regios did indeed share a common point.

    Is there a mathematical term for this or another explaination that makes more sense?
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  4. #4
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    I don't think it is really a math question so much as a question of "what do you mean by 'touch', which is not a standard mathematical term?" Does the interval (0, 1) 'touch' the interval (1, 2)? Does it 'touch' [1, 2]. And a "legal" question: does the border of between two states lie in both states? or in both? or in a specific one of them?
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