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Math Help - Distance between points

  1. #1
    Super Member malaygoel's Avatar
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    Distance between points

    I don't know where to post this question, so I am posting it here.
    Take any n points in a plane and let D and d be the greatest and least distances determined by points of this set. Prove that 2D > sqrt(3) [sqrt(n)-1]d.
    If it is easy, give hint.
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  2. #2
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    malaygoel.
    Please do not make begging posts, everyone can see your question.
    ---
    I was not able to find a way, but I was thinking maybe you can use induction. Assume it works for n then it must work for n+1. The first case with n=3 is clearly true because it leads to,

    2D\geq \sqrt{3}(\sqrt{3}-1)d
    Which is clearly true because,
    D\geq d
    2\geq \sqrt{3}(\sqrt{3}-1)

    But for n=4 I was having difficulty.
    ---
    How do you know that this inequality is true?
    Is it a known theorem?
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