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.
"Optimal Triangulation of Random Samples in the Plane." Ann. Probab. 10 (3) 548 - 553, August, 1982. https://doi.org/10.1214/aop/1176993766