Lognormality and Triangles of Unit Area
Probability
2014-12-22 v1 Metric Geometry
Abstract
To generate a triangle of unit perimeter, break a stick of length 1 in two places at random, with the condition that triangle inequalities are satisfied. Is there a similarly natural method for generating triangles of unit area? Study of a product (rather than a sum) of random lengths is facilitated by closure of multiplication within the lognormal family of distributions. Our (necessarily incomplete) answers to the question each draw upon this property.
Keywords
Cite
@article{arxiv.1412.5860,
title = {Lognormality and Triangles of Unit Area},
author = {Steven R. Finch},
journal= {arXiv preprint arXiv:1412.5860},
year = {2014}
}
Comments
10 pages, 3 figures