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Approximation problems for convex polyhedra

Published online by Cambridge University Press:  26 February 2010

G. C. Shephard
G. C. Shephard
Affiliation:
Department of Pure Mathematics, The University, Birmingham.
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Extract

Let K be any convex body in En, and K any given class of convex sets in En. Then we shall say that K is approximable by the class K if there exists a sequence of sets {Ki}, such that, as i→∞, Ki→K in a suitable metric (for example, the Hausdorff metric), where each set Ki is a vector sum of (a finite number of) sets of the class K An approximation problem is to determine necessary and sufficient conditions for K to be approximable by a given class K.

Type
Research Article
Information
Mathematika , Volume 11 , Issue 1 , June 1964 , pp. 9 - 18
Copyright
Copyright © University College London 1964

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References

1.Blaschke, W., Kreis und Kugel (Veit, Leipzig, 1916). Reprint (Chelsea, New York, 1948).CrossRefGoogle Scholar
2.Bonnesen, T. and Fenchel, W., Theorie der Konvexen Körper (Springer, Berlin, 1934). Reprint (Chelsea, New York, 1948).Google Scholar
3.Grünbaum, B., “Measures of symmetry for convex sets”, Proc. Symposia in Pure Math., VII, Convexity (AMS, 1963).Google Scholar
4.Shephard, G. C., “Convex bodies and convexity on Grassman cones (VIII)”, Journal London Math. Soc., 39 (1964) to appear.Google Scholar
5.Shephard, G. C., “Indecomposable polyhedra”, Mathematika, 10 (1963), 89–95.CrossRefGoogle Scholar
6.Steiner, J., “Von dem Krümmungsschwerpunkte ebener Curven”, J. Heine Angew. Math., 21 (1840), 33–63, 101–122; orGoogle Scholar
Ges. Werke, Bd. 2 (G. Reimer, Berlin, 1882), 99–159.Google Scholar