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Math Help - Euclidean vs Manhattan vs Chebyshev distance question

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    Euclidean vs Manhattan vs Chebyshev distance question

    Imagine three points A,B and C. Is it possible AB>AC in Euclidean distance but AC>AB in Manhattan or Chebyshev distance?
    Or if AB>AC in one distance norm then AB>AC in any other distance norm?
    I will be grateful if you state your source(s).

    Thanks from Greece!
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  2. #2
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    Quote Originally Posted by Mastermind View Post
    Imagine three points A,B and C. Is it possible AB>AC in Euclidean distance but AC>AB in Manhattan or Chebyshev distance?
    Or if AB>AC in one distance norm then AB>AC in any other distance norm?
    I will be grateful if you state your source(s).
    If A = (0,0), B = (6,0) and C = (3,4) then AB>AC in Euclidean distance (because 6>5) but AC>AB in Manhattan distance (because 3+4=7>6).

    If A = (0,0), B = (6,8) and C = (9,0) then AB>AC in Euclidean distance (because 10>9) but AC>AB in Chebyshev distance (because max{6,8}=8<9).
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