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On the number of cylinders touching a ball

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Abstract

The following problem is due to W. Kuperberg. What is the maximum number of non-overlapping unit cylinders (a set in \(\mathbb{E}^3 \) consisting of points whose distance from some line does not exceed 1) that can be simultaneously tangent to a unit ball? In this paper we prove that this number is at most 8. It is conjectured that this number is 6.

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References

  1. Banai, E. and Sloane, N. J. A., ‘Uniqueness of certain spherical codes’, Canad. J. Math. 33 (1981), 437–449.

    Google Scholar 

  2. Blichfeldt, H. F., ‘The minimum value of quadratic forms and the closest packing of spheres’, Math. Ann. 101 (1929), 605–608.

    Google Scholar 

  3. Hoppe, R., ‘Bemerkung der Redaktion’, Arch. Math. Phys. (Grunert) 56 (1874), 307–312.

    Google Scholar 

  4. Kuperberg, W., ‘Problem 3.3’, DIMACS report on Workshop on Polytops and Convex Sets, Rutgers University, January 10, 1990.

  5. Leech, J. and Sloane, N. J. A., ‘Sphere packing and error-correcting codes’, Canad. J. Math. 23 (1971), 718–745.

    Google Scholar 

  6. Odlyzko, A. M. and Sloane, N. J. A., ‘New bounds on the number of unit spheres that can touch a unit sphere in n-dimensions’, J. Combin. Theory Ser. A 26 (1979), 210–214.

    Google Scholar 

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Authors and Affiliations

  1. Vércse u. 24/a, H-1124, Budapest, Hungary

    Aladár Heppes

  2. Department of Geometry, Eötvös Loránd University, Rákóczi út 5, H-1088, Budapest, Hungary

    László Szabó

Authors
  1. Aladár Heppes
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  2. László Szabó
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Heppes, A., Szabó, L. On the number of cylinders touching a ball. Geom Dedicata 40, 111–116 (1991). https://doi.org/10.1007/BF00181656

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  • DOI: https://doi.org/10.1007/BF00181656

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