Using the concept of the convex hull of a set of lines, a dual random triangle is defined by selecting three lines from a parent triangle of lines. The angles of the constructed triangle define the shape; calculation of the shape distribution is described. For a sequence of nested triangles constructed in this way it is shown that there is convergence to collinearity and to the collinear shape distribution derived by Mannion for a sequence of vertex-generated triangles.
Publié le : 2006-02-14
Classification:
convergence of shape,
convexity,
dual triangles,
shape distribution
@article{1141136648,
author = {Gates, John},
title = {The shape of a sequence of dual random triangles},
journal = {Bernoulli},
volume = {12},
number = {2},
year = {2006},
pages = { 55-63},
language = {en},
url = {http://dml.mathdoc.fr/item/1141136648}
}
Gates, John. The shape of a sequence of dual random triangles. Bernoulli, Tome 12 (2006) no. 2, pp. 55-63. http://gdmltest.u-ga.fr/item/1141136648/