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Relationships between widths of a convex body and of an inscribed parallelotope

Published online by Cambridge University Press:  17 April 2009

Marek Lassak
Marek Lassak
Affiliation:
Instytut Matematyki i Fizyki ATR, Bydgoszcz 85–796, Poland, e-mail: lassak@atr.bydgoszcz.pl
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Abstract

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Assume that a parallelotope P is inscribed in a three-dimensional convex body C A conjecture says that , where Wi is the ratio of the width of C to the width of P for the direction perpendicular to the i-th pair of parallel facets of P. We prove three weaker inequalities. One of them is , where a3 denotes the related axial diameter of C.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 133 - 140
Copyright
Copyright © Australian Mathematical Society 2001

References

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