On Minkowski Bodies of Constant Width

  title={On Minkowski Bodies of Constant Width},
  author={P. H. J. Kelly},
A metric set is entire if the addition of any point to the set increases the diameter. A convex body has constant width if all pairs of parallel supporting planes are the same distance apart. These concepts are known to be equivalent in euclidean space. The present paper shows that they are also equivalent in a minkowski space. A proof for this equivalence for the minkowski plane was given by Meissner. He showed also that two curves of the same constant width have the same circumference, and… CONTINUE READING