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.
This is easy to do with a zigzag.
When N=10, the area of this 20-gon is 9 < 10^3/100 = 10
Posted by Jer
on 2016-09-01 13:25:49