Re: [math-fun] convex lattice 11-gon of minimum area

On Fri, Dec 19, 2003 at 11:16:07AM -0500, Dan Hoey wrote:

Here's a better search cutoff than the area bound, though I still don't see how to make the search finite.

Theorem: Any convex lattice N-gon that contains K collinear lattice points (x,y), (x+a,y+b), (x+2a,y+2b), ..., (x+(K-1)a,y+(K-1)b) has area at least (K-1)(ceiling(N/2)-1)/2.

You can get rid of your first lemma by noting that, by an action of SL(2,Z), we can assume WLOG that the points are (x,y), (x+1,y), ... (x+k-1,y) Peace, Dylan