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Barycentric subdivision of triangles and semigroups of Möbius maps

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  26 February 2010

I. Bárány ,
A. F. Beardon  and
T. K. Carne
I. Bárány
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest, P.O.B. 127, 1364, Hungary.
A. F. Beardon
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB
T. K. Carne
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB
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Extract

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).

MSC classification

Secondary: 60D05: Geometric probability and stochastic geometry
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 165 - 171
Copyright
Copyright © University College London 1996

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