A new Pick-type theorem on the hexagonal lattice
Let L be the vertex set of the plane tiling by regular hexagons of a unit area. The paper discusses a ``Pick-type theorem'' for hexagonal lattice polygons P, that is, polygons whose vertices belong to L. It is proved that for certain kinds of hexagonal lattice polygons P the area A(P) of P is given by \(A(P)=b/4+i/2+c/12-1,\) where b is the number of points of L on the boundary of P, i is the number of points of L in the interior of P, and c is the boundary characteristic of P. The restrictions placed on L concern the type and/or length of the intersections of the edges of P with the hexagonal tiles.
scientific article; zbMATH DE number 4042713