The smallest triangular cover for triangles of diameter one
type: Item
instance of: scholarly article
title: The smallest triangular cover for triangles of diameter one
zbMATH Open document ID: 1066.52003
DOI: 10.1007/BF02936039
author: Liping Yuan
author: Ren Ding
published in: Journal of Applied Mathematics and Computing
publication date: 2005-03-10T00:00:00Z
review text: A convex region covers a family \(\mathcal{C}\) of curves if it contains a congruent copy of each curve from \(\mathcal{C}\). In this paper the authors determine the smallest triangle \(T\) similar to a given triangle \(T_0\) which covers the family of all triangles of diameter 1. An exhaustive discussion proves that there exist four triangle similar to \(T_0\) such that, depending on some relations between the angles of \(T_0\), the triangle \(T\) is one of them.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 2143246
zbMATH Keywords: Worm problem
zbMATH Keywords: diameter
zbMATH Keywords: similar
zbMATH Keywords: triangle
zbMATH Keywords: smallest
MaRDI profile type: Publication
cites work: Unsolved problems in geometry
cites work: The smallest convex cover for triangles of perimeter two
cites work: Q4221362
cites work: Q4221395
full work available at URL: https://doi.org/10.1007/bf02936039
OpenAlex ID: W2004710691
description: scientific article; zbMATH DE number 2143246