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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

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