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On a Measure of Asymmetry of Convex Bodies

Published online by Cambridge University Press:  24 October 2008

E. Asplund ,
E. Grosswald  and
B. Grünbaum
E. Asplund
Affiliation:
Institute for Advanced StudyPrinceton New Jersey
E. Grosswald
Affiliation:
Institute for Advanced StudyPrinceton New Jersey
B. Grünbaum
Affiliation:
Institute for Advanced StudyPrinceton New Jersey
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Extract

In the present note we discuss some properties of a ‘measure of asymmetry’ of convex bodies in n-dimensional Euclidean space. Various measures of asymmetry have been treated in the literature (see, for example, (1), (6); references to most of the relevant results may be found in (4)). The measure introduced here has the somewhat surprising property that for n ≥ 3 the n-simplex is not the most asymmetric convex body in En. It seems to be the only measure of asymmetry for which this fact is known.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 217 - 220
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Besicovitch, A. SMeasure of asymmetry of convex curves. J. London Math. Soc. 23 (1948), 237–240.CrossRefGoogle Scholar
(2)Bonnesen, T. and Fenchel, W.Theorie der konvexen Körper (Berlin, 1934).Google Scholar
(3)Eggleston, H. GConvexity. (Cambridge Tracts in Mathematics and Mathematical Physics, no. 47) (Cambridge, 1958).CrossRefGoogle Scholar
(4)Grüunbaum, B. Measures of symmetry for convex sets. Proc. Symposium on Convexity, Seattle 1961. (To be published.)Google Scholar
(5)Macbeath, A. MA compactness theorem for affine equivalence—classes of convex regions. Canadian J. Math. 3 (1951), 54–61.CrossRefGoogle Scholar
(6)Neumann, B. HOn an invariant of plane regions and mass distributions. J. London Math. Soc. 20 (1945), 226–237.CrossRefGoogle Scholar