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On Measures of Symmetry of Convex Bodies

Published online by Cambridge University Press:  20 November 2018

G. D. Chakerian  and
S. K. Stein
G. D. Chakerian
Affiliation:
University of California, Davis
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Let K be a convex body (compact, convex set with interior points) in n-dimensional Euclidean space En, and let V(K) denote the volume of K. Let K′ be a centrally symmetric body of maximum volume contained in K (in fact, K′ is unique; see 2 or 9), and define

c(K) = V(K′)/V(K)

Let

c(n) = inf{c(K) : K ⊂ En}.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 497 - 504
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Fáry, I., Sur la densité des réseaux de domaines convexes, Bull. Soc. Math. France, 78 (1950), 152–161.Google Scholar
2. Fáry, I. and Rédei, L., Der zentralsymmetrische Kern und die zentralsymmetrische Huile von konvexen Körpern, Math. Ann., 122 (1950), 205–220.Google Scholar
3. Grünbaum, B., On intersections of similar sets, Portugal. Math., 18 (1959), 155–164.Google Scholar
4. Gr, B.ünbaum, Measures of symmetry for convex sets, Proc. Symp. Pure Math., Amer. Math. Soc, 7 (1963), 233–270.Google Scholar
5. Hadwiger, H., Vorlesungen über Inhalt, Oberfldche und Isoperimetrie (Berlin, 1957).Google Scholar
6. Krakowski, F., Bemerkung zu einer Arbeit von W. Nohl, Elem. Math., 18 (1963), 60–61.Google Scholar
7. Macbeath, A. M., A compactness theorem for affine equivalence-classes of convex regions, Can. J. Math., 3 (1951), 54–61.Google Scholar
8. Nohl, W., Die innere axiale Symmetrie zentrischer Eibereiche der Euklidischen Ebene, Elem. Math., 17 (1962), 59–63.Google Scholar
9. Stein, S., The symmetry function in a convex body, Pacific J. Math., 6 (1956), 145–148.Google Scholar