The Moser Worm problem and Bellman's Lost in a forest problem.

The Moser Worm problem is the task of finding a (convex) cover of minimum in the plane which contains rotated-translated copy of any curve of length one (a worm) as a subset.

Bellman's Lost in a forest problem is to find the shortest path which ensures an escape from a forest of known shape and size.

The problems are directly related in that the Moser worm problem is equivalent to looking for the shape of a forest of given area which has the longest escape path and any solution to Bellman's problem provides an upper bound for the Moser worm problem.

Geometry problems are often neglected and can be approached with the aid of computational searches.

The Moser Worm problem and Bellman's Lost in a forest problem.

The Moser Worm problem is the task of finding a (convex) cover of minimum area in the plane which contains rotated-translated copy of any curve of length one (a worm) as a subset.

Bellman's Lost in a forest problem is to find the shortest path which ensures an escape from a forest of known shape and size.

The problems are directly related in that the Moser worm problem is equivalent to looking for the shape of a forest of given area which has the longest escape path and any solution to Bellman's problem provides an upper bound for the Moser worm problem.

Although these problems are famous I think that this type of geometry problems is often neglected and can be approached with the aid of computational searches to provide new clues.