Geodesic
Generalized Barycentric Subdivision of a Triangle
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 275-283

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A theorem naturally extending the theorem of Barany, Beardon, and Carne about the density of the classes of similar triangles obtained from a given triangle by applying an infinite series of barycentric subdivisions is proved. 
@article{TM_2002_239_a17,
     author = {A. A. Ordin},
     title = {Generalized {Barycentric} {Subdivision} of a {Triangle}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {275--283},
     publisher = {mathdoc},
     volume = {239},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_239_a17/}
}
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A. A. Ordin. Generalized Barycentric Subdivision of a Triangle. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 275-283. http://geodesic.mathdoc.fr/item/TM_2002_239_a17/