Skip to main content
SpringerLink
Log in

Spheres and Sausages, crystals and catastrophes- and a joint packing theory

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. U. Betke, M. Henk, and J.M. Wills, Finite and infinite packings, J. Reine Angew. Math. (Grelle) 453 (1994), 165–191.

    MATH  MathSciNet  Google Scholar 

  2. U. Betke, M. Henk, and J.M. Wills, Sausages are good packings, Discrete Camp. Geom. 13 (1995), 297–311.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Bakowski, H. Hadwiger, and J.M. Wills, Eine Ungleichung zwischen Volumen, Oberflache und Gitterpunktanzahl konvexer Mengen im n-dimensionalen euklidischen Raum,Math. Z. 127 (1972), 363–364.

    Article  MathSciNet  Google Scholar 

  4. K. Böröczky, Jr. and U. Schnell, Asymptotic shape of finite packings, Can. J. Math., in press.

  5. K. Böröczky, Jr. and U. Schnell, Quasicrystals and parametric density, in press.

  6. K. Böröczky, Jr., and J.M. Wills, Finite sphere packings and critical radii, Beit. Geom. Alg. 38 (1997).

  7. G. Fejes Tóth and W. Kuperberg, Packing and covering with convex sets, in Handbook of Convex Geometry, Amsterdam: North Holland (1993), Chap. 3.3.

  8. P.M. Gruber and C.G. Lekkerkerker, Geometry of Numbers, Amsterdam: North-Holland (1987).

  9. R.L. Graham and N.J.A. Sloane, Penny-packing and two-dimensional codes, Discrete Camp. Geom. 5 (1990), 1–11.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. Gritzmann and J.M. Wills, Finite packing and covering, in Handbook of Convex Geometry, Amsterdam: North-Holland (1993), Chap. 3.4.

  11. P.M. Gandini and A. Zucco, On the sausage catastrophe in 4-space, Mathematika 39 (1992), 274–278.

    Article  MATH  MathSciNet  Google Scholar 

  12. H. Hadwiger, Das Wills’sche Funktional, Monatsh. Math. 79 (1975), 213–221.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. v. Laue, Der Wulffsche Satz für die Gleichgewichtsform von Kristallen, Z. Kristallogr. 105 (1943), 124–133.

    MATH  Google Scholar 

  14. C.A. Rogers, Packing and Covering, Cambridge: Cambridge University Press (1994).

    Google Scholar 

  15. U. Schnell, Periodic sphere packings and Wulff-shape, Mathematika, in press.

  16. M. Senechal Quasicrystals and Geometry, Cambridge Univ. Press, Cambridge (1995).

    MATH  Google Scholar 

  17. N.J.A. Sloane, J.H. Conway, T.D.S. Duff, and R.H. Hardin, Minimal energy clusters of hard sphere, Discrete Camp. Geom. 14 (1995), 237–260.

    Article  MATH  MathSciNet  Google Scholar 

  18. J.M. Wills, Finite sphere packings and sphere coverings, Rend. Semin. Mat. Messina, Ser. 112 (1993), 91–97.

    MathSciNet  Google Scholar 

  19. J.M. Wills, On large lattice packings of spheres, Geom. Dedicata 65 (1997), 117–126.

    Article  MATH  MathSciNet  Google Scholar 

  20. J.M. Wills, Parametric density and Wulff-shape, Mathematika 43 (1996), 229–236.

    Article  MATH  MathSciNet  Google Scholar 

  21. Ch. Zong, Strange Phenomena in Convex and DiscreteGeometry, New York: Springer-Verlag (1996).

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Universität Siegen, Höldeninstrasse 3, D-57068, Siegen, Germany

    J. M. Wills

Authors
  1. J. M. Wills
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. M. Wills.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wills, J.M. Spheres and Sausages, crystals and catastrophes- and a joint packing theory. The Mathematical Intelligencer 20, 16–21 (1998). https://doi.org/10.1007/BF03024394

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03024394

Keywords

Search

Navigation