References
H. F. Blichfeldt, On the minimum value of positive real quadratic forms in 6 variables. Bull. Amer. Math. Soc.31, 386 (1925).
H. F. Blichfeldt, The minimum value of quadratic forms, and the closest packing of spheres. Math. Ann.101, 605–608 (1929).
H. F. Blichfeldt, The minimum value of positive quadratic forms in six, seven and eight variables. Math. Z.39, 1–15 (1935).
J. H.Conway and N. J. A.Sloane, Sphere packings, lattices and groups. Berlin-Heidelberg-New York 1988.
L. FejesTóth, Lagerungen in the Ebene, auf der Kugel und im Raum, 2. Auflage. Berlin-Heidelberg-New York 1972.
C. F. Gauss, Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seber. J. Reine Angew. Math.20, 312–320 (1840).
A. Heppes andL. Szabó, On the number of cylinders touching a ball. Geom. Dedicata40, 111–116 (1991).
J.Horváth, Á. H.Temesvári und I.Závoti, Über Kugeipackungen herum einen Zylinder. Manuscript.
A. Korkin etG. Zolotarev, Sur les formes quadratiques positives quaternaires. Math. Ann.5, 581–583 (1872).
W.Kuperberg, Problem 3.3, DIMACS Workshop on Polytopes and Convex Sets. Rutgers University 1990.
J. Leech andN. J. A. Sloane, Sphere packings and error-correcting codes. Canad. J. Math.23, 718–745 (1971).
C. A.Rogers, Packing and covering. Cambridge 1964.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Szabó, L. On the density of unit balls touching a unit cylinder. Arch. Math 64, 459–464 (1995). https://doi.org/10.1007/BF01197225
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01197225