Thread: Theorem on quadrilaterals

Hi, all. Is this a known theorem, meaning you've seen it stated somewhere? A simple quadrilateral whose minimum distance between vertices is 1 and whose maximum distance is sqrt(2) is a unit square.

Originally Posted by JakeD

Hi, all. Is this a known theorem, meaning you've seen it stated somewhere? A simple quadrilateral whose minimum distance between vertices is 1 and whose maximum distance is sqrt(2) is a unit square.

Since, I never seen it means it is not well know.

Did, you arrive at that result thyself?

Originally Posted by ThePerfectHacker

Since, I never seen it means it is not well know.

Did, you arrive at that result thyself?

Thanks for the reply.

The statement is mine but the idea is not. Someone else is analyzing an algorithm for finding the closest pair out of a set of points. That person wants to prove an equivalent statement: the maximum number of points that can be placed in a unit square is 4 when the minimum distance between points is 1.

It seems obvious but developing a proof has not been. I have one now, but I did not want to bother posting it if this is, say, a well-known exercise from high-school geometry.