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Math Help - Distance between two random Points in a square

  1. #1
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    Distance between two random Points in a square

    Hi,

    I am reading papers at the moment that describe an analysis of overhead of a system and as part of the analysis they estimate the distance between two random points in a square.

    The first paper Iím reading says the distance between two random points in a square is sqrt(2)/3. They didnít say where they got this from but I found a reference listed here:
    http://answers.yahoo.com/question/index?qid=20081027054058AAPMIWO

    The second paper Iím reading also needs the distance between two random points in a square and state that the formula used in paper 1 is used incorrectly (they donít say why). They suggest using the formula which would give a value of 0.521405433 (1/15[sqrt(2) + 2+ 5ln(1+sqrt(2))])....sorry for the notation.
    I found a reference for that here:
    http://mathworld.wolfram.com/SquareLinePicking.html

    Then I read a third paper and they stated that the average geometrical distance between any two random points in a square of side length L is 2L/3.

    Can someone please explain to me which equation is correct and/or why variations might exist (and also if one of these is simply out and out wrong).

    Thanks in advance.
    Kerrymaid.
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  2. #2
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    Quote Originally Posted by kerrymaid View Post
    Hi,

    I am reading papers at the moment that describe an analysis of overhead of a system and as part of the analysis they estimate the distance between two random points in a square.

    The first paper Iím reading says the distance between two random points in a square is sqrt(2)/3. They didnít say where they got this from but I found a reference listed here:
    http://answers.yahoo.com/question/index?qid=20081027054058AAPMIWO Mr F says: Wrong.

    The second paper Iím reading also needs the distance between two random points in a square and state that the formula used in paper 1 is used incorrectly (they donít say why). They suggest using the formula which would give a value of 0.521405433 (1/15[sqrt(2) + 2+ 5ln(1+sqrt(2))])....sorry for the notation.
    I found a reference for that here:
    http://mathworld.wolfram.com/SquareLinePicking.html Mr F says: Correct.

    Then I read a third paper and they stated that the average geometrical distance between any two random points in a square of side length L is 2L/3. Mr F says: Wrong. It probably meant to say that the SQUARE of the average geometrical distance is 2L^2/3.

    Can someone please explain to me which equation is correct and/or why variations might exist (and also if one of these is simply out and out wrong).

    Thanks in advance.
    Kerrymaid.
    ..
    Thanks from lasla
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  3. #3
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    Thats great - thanks for that.
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