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A valuation property of Steiner points

Published online by Cambridge University Press:  26 February 2010

G. T. Sallee
G. T. Sallee
Affiliation:
University of Washington, Seattle, Washington.
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Extract

With each non-empty compact convex subset K of Ed is associated a Steiner point, s(K), defined by

where u is a variable unit vector, a is a fixed unit vector, H(u, K) is the supporting function of K and dw is an element of surface area of the unit sphere Sd-1 centred at the origin (see [2]). For notational convenience, we put s(Ø) = 0.

Type
Research Article
Information
Mathematika , Volume 13 , Issue 1 , June 1966 , pp. 76 - 82
Copyright
Copyright © University College London 1966

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References

1. Grünbaum, B., Convex polytopes, Wiley and Sons, to appear.Google Scholar
2. Shephard, G. C., “Approximation problems for convex polyhedra”, Mathematika, 11 (1964), 9–18.CrossRefGoogle Scholar
3. Shephard, G. C., “The Steiner point of a convex polytope”, Canadian J. of Math., to appear.Google Scholar