Sausage Conjecture

In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a line), independent of the number of n-spheres. The conjecture was proposed by Fejes Tóth, and solved for dimensions >=42 by Betke et al. (1994) and Betke and Henk (1998).

See also

Content, Convex Hull, Hypersphere, Hypersphere Packing, Sphere Packing

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Betke, U. and Henk, M. "Finite Packings of Spheres." Discrete Comput. Geom. 19, 197-227, 1998.Betke, U.; Henk, M.; and Wills, J. M. "Finite and Infinite Packings." J. reine angew. Math. 453, 165-191, 1994.Croft, H. T.; Falconer, K. J.; and Guy, R. K. Problem D9 in Unsolved Problems in Geometry. New York: Springer-Verlag, 1991.Fejes Tóth, L. "Research Problems." Periodica Methematica Hungarica 6, 197-199, 1975.

Referenced on Wolfram|Alpha

Sausage Conjecture

Cite this as:

Weisstein, Eric W. "Sausage Conjecture." From MathWorld--A Wolfram Web Resource.

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