TITLE: The angles subtended in a TSP tour
QUESTION [12 upvotes]: If I sample a large number of uniform points in the unit square and take a traveling salesman tour of them, is there anything at all that can be said/is known about the distribution of angles at each point?  The two pictures below show a TSP tour of 1000 points, together with a histogram of the angles.   
It is intuitive that we expect a lot of angles to be near $\pi$, since an angle close to $0$ (or to $2\pi$) suggests that we're "doubling back" on a route and possibly being inefficient.

REPLY [2 votes]: The distribution has a stunning similarity to the density function of random Delaunay angles mentioned on page 4 of The Expected Extremes in a Delaunay Triangulation

An explanation might be, that optimal tours go along Delaunay edges for a major part of their course (that heuristic made me search for properties of Delaunay triangulations in the first place).