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