Optimal Triangulation of Random Samples in the Plane
John M. Steele · The Annals of Probability · 1982
Let $T_n$ denote the length of the minimal triangulation of $n$ points chosen independently and uniformly from the unit square. It is proved that $T_n/\sqrt n$ converges almost surely to a positive constant. This settles a conjecture of Gyorgy Turan.