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Geometriae Dedicata

, Volume 42, Issue 2, pp 205–213 | Cite as

Small universal covers for sets of unit diameter

  • H. C. Hansen
Article

Abstract

The current smallest convex universal cover for sets of unit diameter is described. This reduction of Sprague's cover is by 4 · 10-11 and results in an asymmetrical cover. Another small universal cover of sets of unit diameter with an axis of symmetry reduces Sprague's cover by 0.0019. An indication is given of how to use computers in the solution of this kind of problem.

Keywords

Universal Cover Small Convex Unit Diameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Pal, J., ‘Über ein elementares Variationsproblem’, Danske Mat.-Fys. Meddelelser III, 2 (1920).Google Scholar
  2. 2.
    Sprague, R., ‘Über ein elementares variationsproblem’, Mat. Tidsskrift (1936), 96–99.Google Scholar
  3. 3.
    Hansen, H. C., ‘A small universal cover of figures of unit diameter’, Geom. Dedicata 4 (1975), 165–172.Google Scholar
  4. 4.
    Duff, G. F. D., ‘A smaller universal cover for sets of unit diameter’, C. R. Math. Acad. Sci. 2 (1980), 37–42.Google Scholar
  5. 5.
    Hansen, H. C., ‘P» vej mod det minimale universelle dæksel’, Normat 29, 3 (1981), 115–119.Google Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • H. C. Hansen
    • 1
  1. 1.Askov HøjskoleVejenDenmark

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