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Barycentric subdivision of triangles and semigroups of Möbius maps
Author(s) -
Bárány I.,
Beardon A. F.,
Carne T. K.
Publication year - 1996
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300011669
Subject(s) - mathematics , subdivision , barycentric coordinate system , mathematical sciences , combinatorics , mathematics education , geometry , geography , archaeology
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).