Distinct equilateral triangle dissections of convex regions

Donovan, Diane M., Lefevre, James G., McCourt, Thomas A. and Cavenagh, Nicholas J. (2012) Distinct equilateral triangle dissections of convex regions. Commentationes Mathematicae Universitatis Carolinae, 53 2: 189-210.

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Name Description MIMEType Size Downloads
Author Donovan, Diane M.
Lefevre, James G.
McCourt, Thomas A.
Cavenagh, Nicholas J.
Title Distinct equilateral triangle dissections of convex regions
Journal name Commentationes Mathematicae Universitatis Carolinae   Check publisher's open access policy
ISSN 0010-2628
1213-7243
Publication date 2012
Sub-type Article (original research)
Open Access Status
Volume 53
Issue 2
Start page 189
End page 210
Total pages 22
Place of publication Prague, Czech Republic
Publisher Matematicko-Fyzikalni Fakulta, Univerzita Karlova v Praze
Language eng
Subject 2600 Mathematics
Formatted abstract
We define a proper triangulation to be a dissection of an integer sided equilateral triangle into smaller, integer sided equilateral triangles such that no point is the vertex of more than three of the smaller triangles. In this paper we establish necessary and sufficient conditions for a proper triangulation of a convex region to exist. Moreover we establish precisely when at least two such equilateral triangle dissections exist.

We also provide necessary and sufficient conditions for some convex regions with up to four sides to have either one, or at least two, proper triangulations when an internal triangle is specified.
Keyword Equilateral triangle dissection
Latin trade
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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