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Minimal requirements for Minkowski's theorem in the plane I

Published online by Cambridge University Press:  17 April 2009

J.R. Arkinstall
J.R. Arkinstall
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia 5001, Australia.
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Abstract

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Let K be a closed convex set in the Euclidean plane, with area A(K), which contains in its interior only one point 0 of the integer lattice. If K has other than one or three chords bisected by 0, it is shown that A(K) ≤ 4. Also, if K has three such chords, A(K) ≤ 4.5. The results are generalised to any lattice in the plane.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 2 , October 1980 , pp. 259 - 274
Copyright
Copyright © Australian Mathematical Society 1980

References

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