Given a planar polygon (or chain) with a list of edges e1, e2, e3,..., e 1, e, we examine the
effect of several operations that this edge list, resulting in the formation of a new polygon …

A hiker is lost in a forest of unknown shape. What is a good path for the hiker to follow in
order to escape from the forest within a reasonable amount of time? The hiker's dilemma …

This thesis considers four search problems which are related to or emerge from a geometric
context. Each search problem is examined in a separate chapter; these four chapters are …

More than fifty years ago, Bellman asked for the best escape path within a known forest but
for an unknown starting position. This deterministic finite path is the shortest path that leads …

Given a planar polygon (or chain) with a list of edges {e1, e2, e3,…, en-1, en}, we examine
the effect of several operations that permute this edge list, resulting in the formation of a new …

We search for the shortest curve in the plane that does not fit inside some given polygon.
This generalizes the “river shore” problem to the “lake shore” problem. We give solutions for …