[1] The problem is often stated as follows: "A hiker is lost in a forest whose shape and dimensions are precisely known to him.
The best path is taken to be the one that minimizes the worst-case distance to travel before reaching the edge of the forest.
In particular, all shapes which can enclose a 60° rhombus with longer diagonal equal to the diameter have a solution of a straight line.
The equilateral triangle is the only regular polygon which does not have this property, and has a solution consisting of a zig-zag line with three segments of equal length.
[4] A general solution would be in the form of a geometric algorithm which takes the shape of the forest as input and returns the optimal escape path as the output.