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Equipartition of convex bodies

Published online by Cambridge University Press:  17 April 2009

Paul R. Scott
Paul R. Scott
Affiliation:
Department of Mathematics, University of Adelaide, Adelaide SA 5001, Australia
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Abstract

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We show that a compact convex body in En cannot be partitioned by n + 1 hyperplanes into 2n+l – 1 subsets of equal measure, thus generalising a result in the plane due to R.C. and E.F. Buck.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 141 - 144
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Buck, R.C. and Buck, E.F., ‘Equipartition of convex sets’, Math. Mag. 22 (1948), 195–198.CrossRefGoogle Scholar
[2]Eggleston, H.G., Problems in Euclidean space: application of convexity, pp. 126–129 (Pergamon Press, 1957).Google Scholar
[3]Sholander, M., ‘Proof of a conjecture by R.C. and E.F. Buck’, Math. Mag. 24 (1950), 8–10.CrossRefGoogle Scholar