Convex lattice polygons of minimum area

Abstract

A convex lattice polygon is a polygon whose vertices are points on the integer lattice and whose interior angles are strictly less than π radians. We define a ( 2n ) to be the least possible area of a convex lattice polygon with 2n vertices. A method for constructing convex lattice polygons with area a ( 2n ) is described, and values of a ( 2n ) for low n are obtained.