Median Area for Broken Sticks
arXiv:1804.09602
Abstract
Breaking a line segment L in two places at random, the three pieces can be configured as a triangle T with probability 1/4. We determine both the PDF and CDF for area(T) in terms of elliptic integrals. In particular, if L has length 1, then the median area 0.031458... can be calculated to arbitrary precision. We also mention the analog involving cyclic quadrilaterals -- with corresponding probability 1/2 -- and ask some unanswered questions.
13 pages; 6 figures