English

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

R2 v1 2026-06-22T07:36:52.873Z