Some Properties Of N-segment Unit Arc In The Plane

Let Fnbe the family of all n-segment unit arcs. For each n=2,3,..., let t_n=sup{t(γ):γ∈F_n} be the broadest n-segment unit. An n-segment unit arc with breadth t_niscalled the broadest n-segment unit arc. An arc is convex if it is simple and it lies on theboundary of its convex hull. A convex arc with distinct endpoints P and Q is a drape ifit lies in a closed semi-infinite strip bounded by the endpoint line segment PQ and therays perpendicular to PQ at the endpoints P and Q. This thesis prove three open problemsin[10]: the broadest n-segment unit arc is convex; the broadest n-segment unit arc is adrape; the sequence of breadths tnstrictly increases.