A new Pick-type theorem on the hexagonal lattice
type: Item
instance of: scholarly article
title: A new Pick-type theorem on the hexagonal lattice
zbMATH Open document ID: 0639.52011
DOI: 10.1016/0012-365X(88)90110-0
author: Ren Ding
author: John R. Reay
author: Krzysztof Kołodziejczyk
published in: Discrete Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 4042713
zbMATH Keywords: plane tiling
zbMATH Keywords: Pick-type theorem
zbMATH Keywords: hexagonal lattice polygons
zbMATH Keywords: area
reviewed by: Egon Schulte
MaRDI profile type: Publication
cites work: The boundary characteristic and Pick's theorem in the Archimedean planar tilings
cites work: Pick's Theorem Revisited
description: scientific article; zbMATH DE number 4042713