I misunderstood. when you said
> Adding points to the set can only ever shrink the size of the smallest triangle that the set defines.
I thought you meant, adding points would shrink the size of the smallest triangle. Rereading the thread and the article, (I think you mean) The only possible effect (if there is any effect at all) of adding points is is to shrink the size of the smallest triangle.
I was thinking of a 10x10 square, and points at (0,0) (0,1) (1,1) - adding a point at 5,10 has no effect on the smallest triangle, but you could add a point at 10,10, and get a line, area zero.
I thought you meant, adding points would shrink the size of the smallest triangle. Rereading the thread and the article, (I think you mean) The only possible effect (if there is any effect at all) of adding points is is to shrink the size of the smallest triangle.
I was thinking of a 10x10 square, and points at (0,0) (0,1) (1,1) - adding a point at 5,10 has no effect on the smallest triangle, but you could add a point at 10,10, and get a line, area zero.
Thanks for the thoughtful reply.