Suppose I have a polygonal field with a post at each vertex and a non-extensible rope threaded through each post around the perimeter but with some slack. How can I determine the perimeter of the area reachable by a goat tethered to the rope?
Once the rope is tight against two posts I believe that part of the perimeter will be a semi-ellipse but I can't see how to determine the (varying) length of slack available at different points, or how to handle concave/convex posts.