Steele, J Michael2023-05-232023-05-2319822017-08-24https://repository.upenn.edu/handle/20.500.14332/47659Let Tn denote the length of the minimal triangulation of n points chosen independently and uniformly from the unit square. It is proved that Tn/√n converges almost surely to a positive constant. This settles a conjecture of György Turán.The original and published work is available at: https://projecteuclid.org/euclid.aop/1176993766#abstracttriangulationprobabilistic algorithmsubadditive Euclidean functionalsjackknifeEfron-Stein inequalityPhysical Sciences and MathematicsArticle