INFINITE PATHS WITH NO SMALL ANGLES
Imre Bárány, Attila Pór · Mathematika · 2009
It is shown here that given a discrete (and infinite) set of points in the plane, it is possible to arrange them on a polygonal path so that every angle on the polygonal path is at least 9∘. This has been known to hold for finite sets (with 20∘). The main result holds for discrete sets in higher dimensions as well, with a smaller bound on the angle.