Fencing next to a river

Originally posted by PBE6
Just checked Wikipedia under "cyclic polygons"...apparently any triangle, quadrilateral or simple regular polygon is cyclic, but it's mute on polygons with 5 sides or more (I'm assuming this is because it's not always true for them, but I have no proof).

This is correct, not all polygons with 5 or more sides are cyclic (since some are concave). You can construct a cyclic polygon from n arbitrary edge lengths by placing the vertices on a circle and fixing the linear distances between the vertices to be the same as (n - 1) of the edge lengths. If you then change the radius of the circle, as the vertices move around you will find a circle that will allow you to fit in the last edge. This means that for an arbitrary set of edge lengths you can always find at least one polygon that is cyclic.