A short proof of the twelve-point theorem

Autor:	Mikhail Skopenkov, Matija Cencelj, Dušan Repovš
Rok vydání:	2005
Předmět:	Combinatorics High Energy Physics::Lattice General Mathematics Elementary proof Lattice (group) Boundary (topology) Point (geometry) Dual polygon Convex polygon Mathematics
Zdroj:	Mathematical Notes. 77:108-111
ISSN:	1573-8876 0001-4346
DOI:	10.1007/s11006-005-0010-6
Popis:	We present a short elementary proof of the following twelve-point theorem. Let M be a convex polygon with vertices at lattice points, containing a single lattice point in its interior. Denote by m (respectively, m*) the number of lattice points in the boundary of M (respectively, in the boundary of the dual polygon). Then m + m* = 12.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::dbdf12f8b9f05d63df0f192f59b802ca https://doi.org/10.1007/s11006-005-0010-6 Zobrazit plný text záznamu Plný text ve formátu PDF