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Math Help - violation of triangular inequality

  1. #1
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    Smile violation of triangular inequality

    Hi i need 3 points that violate the triangular inequality, tryed many just can't seem to find it.

    the inequality is d(p,r) less or equal to d(p,q)+d(q,r) so to violate it i need d(p,r) to be greater than the sum of d(p,q)+d(q,r)
    where d is the distance...

    Thanks !
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  2. #2
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    Ok Nikie; triangle ABC has sides AB=3, AC=4 and BC=8 : any comments?
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  3. #3
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    Quote Originally Posted by Wilmer View Post
    Ok Nikie; triangle ABC has sides AB=3, AC=4 and BC=8 : any comments?
    Yes, i need three points so when i plug them into the distance formula i can get those distances for each side
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  4. #4
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    Hello nikie1o2
    Quote Originally Posted by nikie1o2 View Post
    Hi i need 3 points that violate the triangular inequality, tryed many just can't seem to find it.

    the inequality is d(p,r) less or equal to d(p,q)+d(q,r) so to violate it i need d(p,r) to be greater than the sum of d(p,q)+d(q,r)
    where d is the distance...

    Thanks !
    I'm not sure what you mean here. The inequality holds good in all Euclidean spaces, so how are you hoping to find points that violate it?

    Grandad
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  5. #5
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    Quote Originally Posted by nikie1o2 View Post
    Yes, i need three points so when i plug them into the distance formula i can get those distances for each side
    Forget that...I'll ask the question this way:
    Ok Nikie; triangle ABC has sides AB=3, AC=4 and BC=8.
    Can you draw that triangle?
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  6. #6
    Member mohammadfawaz's Avatar
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    If you can find such three points in a Euclidean space, then you just proved that all theorems based on this inequality are wrong, and believe me..there are many!
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