Vertex polygons
type: Item
instance of: scholarly article
title: Vertex polygons
zbMATH Open document ID: 1275.51013
author: Candice Nielsen
published in: Involve
publication date: 2013-05-28T00:00:00Z
full work available at URL: p12.xhtml
review text: Given an \(m\)-sided polygon, a vertex \(n\)-gon is an \(n\)-sided polygon formed using \(n\) vertices of the \(m\)-sided polygon. An equal-\(n\)-gon polygon is a polygon, for which all vertex \(n\)-gons have the same non-zero area. The definitions are generalizations of vertex triangles and equal-area polygons introduced by \textit{G. Harel} and \textit{J. M. Rabin} [Am. Math. Mon. 110, No. 7, 606--619 (2003; Zbl 1046.51008)]. The author proves a result that gives necessary conditions for an equal-area hexagon to be also equal-quadrilateral. Furthermore, a method to construct equal-quadrilateral hexagons is given and extended to equal-\((n+1)\)-gon polygons.
reviewed by: Dimitris P. Vartziotis
Mathematics Subject Classification ID: 51N20
Mathematics Subject Classification ID: 00A99
zbMATH DE Number: 6167075
zbMATH Keywords: vertex polygons
zbMATH Keywords: vertex triangles
zbMATH Keywords: vertex quadrilaterals
zbMATH Keywords: equal-\(n\)-gon polygon
zbMATH Keywords: equal-area hexagon
zbMATH Keywords: equal-quadrilateral hexagons
MaRDI profile type: Publication
OpenAlex ID: W4250666132
DOI: 10.2140/INVOLVE.2012.5.361
description: scientific article; zbMATH DE number 6167075