Lognormality and Triangles of Unit Area
  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. 
Steven R. Finch
math.PR math.MG