2018/04/25 by Steven R. Finch, Finch, Steven R.
Computer Science · Engineering · Mathematics · #51M25 #52A22 #52A38 (Secondary) #60D05 (Primary) 51M04 #62E15 #62H10 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1804.09602
openalex publication_date 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.