Packing Cones and Their Negatives in Space |
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| Authors: | Imre Barany Jiri Matousek |
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| Institution: | (1) Renyi Institute of Mathematics, Hungarian Academy of Sciences, PO Box 127, 1364 Budapest, Hungary and Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England;(2) Department of Applied Mathematics and Institute of Theoretical Computer Science (ITI), Charles University, Malostranske nam. 25, 118 00 Praha 1, Czech Republic |
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| Abstract: | Let C be a cone in R3 whose base B is a planar convex body in a horizontal plane π and whose tip is a point v ∉ π. Let C be a packing formed by translates of C and -C in R3. We exhibit an explicit constant c > 0 such that the density of any such C is smaller than 1 - c, answering a question of Wlodek Kuperberg. |
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