A convex polygon having precisely 2N (N ≥2) sides has each of its vertices at lattice points.

Can the area of the polygon be < N³/100?
If so, give an example.
If not, prove it.

Before even looking for a solution it stands to reason that since the limit grows as a cubic, all we need to do is find a way of increasing the area as a lower degree function of N and a solution will occur.

Posted by Jer on 2016-09-01 13:25:49