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Connectivity and freely rolling convex bodies
Author(s) -
Goodey P. R.
Publication year - 1982
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/s002557930001233x
Subject(s) - mathematics , ball (mathematics) , regular polygon , translation (biology) , rotation (mathematics) , combinatorics , convex body , geometry , topology (electrical circuits) , pure mathematics , convex hull , chemistry , biochemistry , messenger rna , gene
If C and C o are two convex bodies in E d we say that C slides (rolls) freely inside C o if the following condition is satisfied: for each x ∈ ∂ C 0 (and each rotation R ) there is a translation t such that, if gC = C + t (= RC + t ), then gC ⊂ C o and x ∈ ∂ gC . This work establishes certain topological conditions which ensure the free rolling and sliding of C inside C o . One consequence of these conditions is that, if ∂ K ∩ int gK is a topological ball for all rigid motions g , then K is a ball in the geometrical sense.