Barany, I; Beardon, AF; Carne, TK; (1996) Barycentric subdivision of triangles and semigroups of Mobius maps. MATHEMATIKA , 43 (1) 165 - 171. 10.1112/S0025579300011669.
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The following question of V. Stakhovskii was passed to us by N. Dolbilin . Take the barycentric subdivision of a triangle to obtain six triangles, then take the barycentric subdivision of each of these six triangles and so on; is it true that the resulting collection of triangles is dense (up to similarities) in the space of all triangles? We shall show that it is, but that, nevertheless, the process leads almost surely to a flat triangle (that is, a triangle whose vertices are collinear).
|Title:||Barycentric subdivision of triangles and semigroups of Mobius maps|
|Keywords:||SEQUENCE, SHAPES, Geometric probability|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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