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The Steiner Point of a Convex Polytope

Published online by Cambridge University Press:  20 November 2018

G. C. Shephard
G. C. Shephard*
Affiliation:
University of Washington, Seattle, U.S.A. and University of Birmingham, England
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Associated with each bounded convex set K in n-dimensional euclidean space En is a point s(K) known as its Steiner point. First considered by Steiner in 1840 (6, p. 99) in connection with an extremal problem for convex regions, this point has been found useful in some recent investigations (for example, 4) because of the linearity property

1

Addition on the left is vector addition of convex sets.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1294 - 1300
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Anderson, R. D. and Klee, V., Continuous functions and upper semi-continuous collections, Duke Math. J., 19 (1952), 349–357.Google Scholar
2. Bonnesen, T. and Fenchel, W., Konvexe Körper (New York, 1948).Google Scholar
3. Grünbaum, B., Convex polytopes (to be published).Google Scholar
4. Shephard, G. C., Approximation problems jor convex polyhedra, Mathematika, 11 (1964), 9–18.Google Scholar
5. Sommerville, D. M. Y., An introduction to the geometry of n dimensions (New York, 1958).Google Scholar
6. Steiner, J., Gesammelte Werke, 2 vols. (Berlin, 1881, 1882).Google Scholar