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On Plane Sections and Projections of Convex Sets

Published online by Cambridge University Press:  20 November 2018

H. Groemer
H. Groemer*
Affiliation:
The University of Arizona, Tucson, Arizona
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Let K be a three-dimensional convex body. It has been conjectured (cf. 3) that one can always find a plane H such that the intersection K ∩ H is, in a certain sense, fairly circular. Instead of the plane section K ∩ H one can also consider the orthogonal projection of K onto H. Our aim in this paper is to prove some results concerning this type of problems. It appears that John has found similar theorems (cf. the remarks of Behrend, 1, p. 717). His proof of the first inequality of our Theorem 1 has been published (6). It is based on a property of the ellipse of inertia which will not be used in the present paper.

A non-empty compact convex set 5 which is contained in some plane of euclidean three-dimensional space E3 will be called a convex domain.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1331 - 1337
Copyright
Copyright © Canadian Mathematical Society 1969

References

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