Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 37 (1996), No. 1, 1-8.

Two Problems Concerning the Area-perimeter Ratio of Lattice-point-free
Regions in the Plane

Uwe Schnell and Salvador Segura Gomis

Abstract

  We give a generalization of Bender's area-perimeter relation for
  plane lattice-point-free convex regions to simply connected regions,
  thus we solve a problem posed by M.~Silver [10].
  Further the result is used for a lattice version of the Dido problem.

  MSC 1991: 52C05, 11H06