Open Access
2009 Tesselation of a triangle by repeated barycentric subdivision
Robert Hough
Author Affiliations +
Electron. Commun. Probab. 14: 270-277 (2009). DOI: 10.1214/ECP.v14-1471


Under iterated barycentric subdivision of a triangle, most triangles become flat in the sense that the largest angle tends to $\pi$. By analyzing a random walk on $SL_2(\mathbb{R})$ we give asymptotics with explicit constants for the number of flat triangles and the degree of flatness at a given stage of subdivision. In particular, we prove analytical bounds for the upper Lyapunov constant of the walk.


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Robert Hough. "Tesselation of a triangle by repeated barycentric subdivision." Electron. Commun. Probab. 14 270 - 277, 2009.


Accepted: 5 July 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60031
MathSciNet: MR2516262
Digital Object Identifier: 10.1214/ECP.v14-1471

Primary: 60D05
Secondary: 52B60 , 52C45 , 60J10

Keywords: Barycentric subdivision , Random walk on a group

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