This column is devoted to non-crossing configurations in the plane realized with straight line segments connecting pairs of points from a finite ground set. Graph classes of interest realized in this way include matchings, spanning trees, spanning cycles, and triangulations. We review some problems and results in this area. At the end we list some open problems.

We consider four problems connected by the common thread of geometry. The first three arise in applications that apriori do not involve geometry but this turns out to be the right language for visualizing and analyzing them. In the fourth, we generalize some well known results in geometry to the topological plane. The techniques we use come from probability and topology. First, we consider two ...

background and objectives: pomegranate juice (pj) contains large particles that stick to evaporator walls causing off flavors in the concentrate due to burning. microfiltration is used to clarify pj. fouling is a limiting phenomenon that can prevent the industrialization of membrane clarification. changes in the geometry of the membrane module such as using baffles are useful to decrease this p...