On characterizing collections arising from N-gons in the plane
type: Item
instance of: scholarly article
title: On characterizing collections arising from N-gons in the plane
zbMATH Open document ID: 0703.52001
DOI: 10.1007/BF00147603
author: Paul Edelman
author: D. G. Larman
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: Consider a convex n-gon P in the plane with vertices labelled 1,...,n and a point x in general position in the interior of P. With P and x is associated the collection \({\mathcal F}(x)\) of all 3-element sets \(\{\) i,j,k\(\}\) of \(\{\) 1,...,n\(\}\) for which x lies in the triangle with vertices labelled i, j, k. The authors completely characterize those collections of 3-element subsets of \(\{\) 1,...,n\(\}\) which can arise this way. They also give a characterization for a related problem.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A01
zbMATH DE Number: 4153339
zbMATH Keywords: axiomatic convexity
zbMATH Keywords: Carathéodory's theorem
zbMATH Keywords: convex n-gon
zbMATH Keywords: collections of 3-element subsets
reviewed by: Egon Schulte
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147603
OpenAlex ID: W2042735404
description: scientific article; zbMATH DE number 4153339