Partitions of planar sets into small triangles
type: Item
instance of: scholarly article
title: Partitions of planar sets into small triangles
zbMATH Open document ID: 0591.52004
DOI: 10.1016/0012-365X(85)90158-X
author: Andrew Odlyzko
author: Kenneth B. Stolarsky
author: János Pintz
published in: Discrete Mathematics
publication date: 1985-01-01T00:00:00Z
review text: For a set P of 3n points in a convex planar body \(\Sigma\), a(n,P,\(\Sigma)\) is the smallest sum of areas of n triangles formed by the points P, such that the vertices of the triangles exhaust the 3n points of P and the triangles are pairwise disjoint. If a(n,\(\Sigma)\) denotes the supremum of a(n,P,\(\Sigma)\) over all \(P\subset \Sigma\) of 3n points, and a(n) denotes the supremum of a(n,\(\Sigma)\)/A(\(\Sigma)\) over all convex planar sets \(\Sigma\) with positive area A(\(\Sigma)\), then for \(n\geq 2\) the following is established \[ n^{-1/2}\ll a(n)\leq 0.8+O(n^{-1})\leq 0.9. \] Open problem: What is the limit of a(n) for \(n\to \infty ?\)
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 51A20
zbMATH DE Number: 3949171
zbMATH Keywords: disjoint triangle partition
zbMATH Keywords: Heilbronn triangle problem
zbMATH Keywords: Ham
zbMATH Keywords: Sandwich theorem
zbMATH Keywords: convex planar body
MaRDI profile type: Publication
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full work available at URL: 0012-365x(85)90158-x
OpenAlex ID: W2087146362
description: scientific article; zbMATH DE number 3949171