On a covering problem for equilateral triangles
type: Item
instance of: scholarly article
title: On a covering problem for equilateral triangles
zbMATH Open document ID: 1160.52014
author: Adrian Dumitrescu
author: Minghui Jiang
published in: The Electronic Journal of Combinatorics
publication date: 2009-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/129864
full work available at URL: v15i1r37.html
review text: Summary: Let \(T\) be a unit equilateral triangle, and \(T_1,\dots,T_n\) be \(n\) equilateral triangles that cover \(T\) and satisfy the following two conditions: (i) \(T_i\) has side length \(t_i (0<t_i<1)\); (ii) \(T_i\) is placed with each side parallel to a side of \(T\). We prove a conjecture of Zhang and Fan asserting that any covering that meets the above two conditions (i) and (ii) satisfies \(\sum_{i=1}^n t_i \geq 2\). We also show that this bound cannot be improved.
Mathematics Subject Classification ID: 52C15
zbMATH DE Number: 5540942
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5540942