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Tesselation of a triangle by repeated barycentric subdivision

  
@article{ECP1471,
	author = {Robert Hough},
	title = {Tesselation of a triangle by repeated barycentric subdivision},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {14},
	year = {2009},
	keywords = {Barycentric subdivision; random walk on a group},
	abstract = {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.},
	pages = {no. 27, 270-277},
	issn = {1083-589X},
	doi = {10.1214/ECP.v14-1471},    
        url = {http://ecp.ejpecp.org/article/view/1471}}