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On the sausage catastrophe in 4‐space
Author(s) -
Gandini Pier Mario,
Zucco Andreana
Publication year - 1992
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015011
Subject(s) - mathematics , unit sphere , euclidean space , ball (mathematics) , combinatorics , regular polygon , integer (computer science) , space (punctuation) , euclidean geometry , convex body , upper and lower bounds , unit (ring theory) , geometry , mathematical analysis , convex hull , linguistics , philosophy , mathematics education , computer science , programming language
Summary An upper bound for the “sausage catastrophe” of dense sphere packings in 4‐space is given. A basic problem in the theory of finite packing is to determine, for a given positive integer k , the minimal volume of all convex bodies into which k translates of the unit ball B d of the Euclidean d ‐dimensional space E d can be packed ([5]). For d = 2 this problem was solved by Groemer ([6]).