ISSN:
1432-0444
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract. When C is a ball in ${\Bbb R}^d$ and S is the sphere $\partial C$ , we say that S supports a convex body B if S intersects B and either $B\subseteq C$ (then S is a far support) or the interior of C is disjoint from B (then S is a near support). The focus here is on common supports for a system $\cal B$ of d+1 bodies in ${\Bbb R}^d$ such that for each way of selecting a point from each member of ${\cal B}$ , the selected points are affinely independent and hence form the vertex-set of a d-simplex. The main result asserts that if $({\cal B}',{\cal B}'')$ is an arbitrary partition of ${\cal B}$ , then there exists a unique Euclidean sphere that is simultaneously a near support for each member of ${\cal B}'$ and a far support for each member of ${\cal B}''$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00009324
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