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A problem concerning three-dimensional convex bodies

Published online by Cambridge University Press:  24 October 2008

R. A. Rankin
R. A. Rankin
Affiliation:
The UniversityBirmingham 15
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Extract

1. The problem considered in this paper arose during an investigation of what Chabauty has called the ‘anomaly’ of convex bodies.

Throughout the paper denotes a closed bounded convex body in three-dimensional Euclidean space , which is symmetric in the origin O and which contains O as an interior point. Such a body determines uniquely a distance-function f(x, y, z) which is defined and finite for each point (x, y, z) of and possesses the following properties

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 44 - 53
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Bonnesen, T. and Fenchel, W.Theorie der konvexen Körper (New York, 1948), §25.Google Scholar
(2)Rankin, R. A.The anomaly of convex bodies. Proc. Camb. phil. Soc. 49 (1953), 54.CrossRefGoogle Scholar