Atlas: Almost-tiling the plane by ellipses by Krystyna Kuperberg

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Spring General Topology & Dynamic Systems Conference
March 16-19, 2000
University of the Incarnate Word and The University of Texas at San Antonio
San Antonio, TX, USA

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Almost-tiling the plane by ellipses
by
Krystyna Kuperberg
Auburn University
Coauthors: W. Kuperberg, J. Matousek, P. Valtr

A collection C of topological closed disks in the plane is a packing if the interiors of the disks are pairwise disjoint. A planar set is centrally symmetric if it is symmetric with respect to a point. For a d > 1, the d-enlargement of a packing of centrally symmetric disks is the collection of d-homothetic copies of the disks with respect to their centers of symmetry. We show that for every d > 1 there exists a periodic and locally finite packing of the plane with ellipses whose d-enlargement covers the whole plane. This answers a question of I. Bárány. We also show that if C is a packing in the plane with circular discs of radius at most 1, then its 1.00001-enlargement covers no square with side length 4. These are joint results of K. Kuperberg, W. Kuperberg, J. Matousek, and P. Valtr. A copy of the paper can be found at http://xxx.lanl.gov/abs/math.MG/9804040 (or, equivalently, at http://front.math.ucdavis.edu/math.MG/9804040).

http://www.auburn.edu/~kuperkm/

Date received: January 18, 2000