On various properties of polygons and some consequences of these properties

Jit Bose, School of Computer Science, Carleton University

I will talk about how enforcing certain "local" properties on points in a simple polygon often cause the existence of some "global" properties. A simple example is the following: If every point in a simple polygon can see the vertices of the polygon, then the polygon is convex. We will also see some examples where one might expect some "global" properties to exist given a set of "local" properties when in fact the "global" properties do not have to exist. Finally, time permitting, we will see an example of a "local" property that implies the existence of a constant number of guards to guard a simple polygon.