A Lower Bound for Lebesgue's Universal Cover Problem

@article{Bra2005ALB,
  title={A Lower Bound for Lebesgue's Universal Cover Problem},
  author={Peter Bra\ss and Mehrbod Sharifi},
  journal={Int. J. Comput. Geometry Appl.},
  year={2005},
  volume={15},
  pages={537-544}
}
In the following we show that any convex set that contains a congruent copy of any set of diameter one (universal cover) has area at least 0.832. This considerably improves the lower bound for Lebesgue's universal cover problem, using a combination of computer search and geometric bounds. 

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 12 references

The classical worm problem—a status

  • J. E. Wetzel
  • report, Geombinatorics
  • 2005

The minimum mean width translation cover for sets of diameter one

  • K. Bezdek, R. Connelly
  • Beitrdge Algebra Geom
  • 1998
1 Excerpt

Generalized breadths, Cantor-type arrangements and the least area UCC

  • G. Elekes
  • Discrete Comput. Geom
  • 1994
1 Excerpt

Small universal covers for sets of unit diameter

  • H. C. Hansen
  • Geometriae Dedicata
  • 1992

Towards the minimal universal cover (in Danish)

  • H. C. Hansen
  • Normat
  • 1981

A smaller universal cover for sets of unit diameter

  • G.F.D. Duff
  • C. R. Math. Rep. Acad. Sci. Canada
  • 1980

A small universal cover of figures of unit diameter

  • H. C. Hansen
  • Geometriae Dedicata
  • 1975

Ungeloste und Unlosbare Prohleme der Geometrie, Priedrich Vieweg und Sohn, Braunschweig 1960; English Translation: Unsolved and Unsolvable Problems in Geometry (Oliver and Boyd 1966)

  • H. Meschkowski
  • 1966

Minimal universal covers in E, Israel

  • H. G. Eggleston
  • J. Math
  • 1963

A pp l

  • R. Sprague, B Mat.Tidsskr.Ser.
  • 1936

Similar Papers

Loading similar papers…