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Almost-Tiling the Plane by Ellipses

Discrete & Computational Geometry, 1999, Vol.22(3), pp.367-375 [Peer Reviewed Journal]

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  • Title:
    Almost-Tiling the Plane by Ellipses
  • Author: Kuperberg, K. ; Kuperberg, W. ; Matoušek, J. ; Valtr, P.
  • Found In: Discrete & Computational Geometry, 1999, Vol.22(3), pp.367-375 [Peer Reviewed Journal]
  • Subjects: Side Length ; Circular Disk ; Finite Packing
  • Language: English
  • Description: For any λ > 1 we construct a periodic and locally finite packing of the plane with ellipses whose λ -enlargement covers the whole plane. This answers a question of Imre Bárány. On the other hand, we show that if C is a packing in the plane with circular disks of radius at most 1, then its (1+16 -5 ) -enlargement covers no square with side length 4.
  • Identifier: ISSN: 0179-5376 ; E-ISSN: 1432-0444 ; DOI: 10.1007/PL00009466

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