## The Annals of Probability

### Optimal Triangulation of Random Samples in the Plane

J. Michael Steele

#### Abstract

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.

#### Article information

Source
Ann. Probab., Volume 10, Number 3 (1982), 548-553.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993766

Digital Object Identifier
doi:10.1214/aop/1176993766

Mathematical Reviews number (MathSciNet)
MR659527

Zentralblatt MATH identifier
0486.60015

JSTOR