Distance between points

• June 5th 2006, 07:00 AM
malaygoel
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.
• June 6th 2006, 12:06 PM
ThePerfectHacker
malaygoel.
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,
$2D\geq \sqrt{3}(\sqrt{3}-1)d$
$D\geq d$
$2\geq \sqrt{3}(\sqrt{3}-1)$
But for $n=4$ I was having difficulty.