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Barycentric subdivision of triangles and semigroups of Mobius maps

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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Abstract

The following question of V. Stakhovskii was passed to us by N. Dolbilin [4]. 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).

Type:Article
Title:Barycentric subdivision of triangles and semigroups of Mobius maps
DOI:10.1112/S0025579300011669
Publisher version:http://dx.doi.org/10.1112/S0025579300011669
Language:English
Keywords:SEQUENCE, SHAPES, Geometric probability
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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