The three vertices of a triangle are lattice points. The triangle contains no other lattice points but its interior contains exactly one lattice point.

Prove that the interior lattice point is the triangle's centroid.

There is only one way to draw a triangle whose vertices are lattice points, whose edges have no lattice points, and whose interior has one lattice point.  That is to start with a 2 X 2 square, place one vertex on a corner and the other two at the midpoint of the non-adjacent sides.

Posted by Steve Herman on 2011-04-11 01:25:53