Sausage Conjecture

In -D for the arrangement of Hyperspheres whose Convex Hull has minimal Contentis always a ``sausage'' (a set of Hyperspheres arranged with centers along a line), independent of the numberof -spheres. The Conjecture was proposed by Fejes Tóth, and solved for dimensions by Betke et al. (1994) and Betke and Henk (1998).

References

Betke, U.; Henk, M.; and Wills, J. M. ``Finite and Infinite Packings.'' J. Reine Angew. Math. 453, 165-191, 1994.

Betke, U. and Henk, M. ``Finite Packings of Spheres.'' Discrete Comput. Geom. 19, 197-227, 1998.

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.

• Padé Conjecture
• Painlevé Property
• Painlevé Transcendents
• Pair
• Paired t-Test
• Pair Sum
• Paley Class
• Paley Construction
• Paley's Theorem
• Palindrome Number
• Palindromic Number
• Palindromic Number Conjecture
• Pancake Cutting
• Pancake Theorem
• Pandiagonal Square
• Pandigital
• Panmagic Square
• Pantograph
• Papal Cross
• Pappus Chain
• Pappus-Guldinus Theorem
• Pappus's Centroid Theorem
• Pappus's Harmonic Theorem
• Pappus's Hexagon Theorem
• Pappus's Theorem