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An isoperimetric problem with lattice point constraints

Part of: General convexity

Published online by Cambridge University Press:  09 April 2009

J. R. Arkinstall  and
P. R. Scott
J. R. Arkinstall
Affiliation:
Department of Pure MathematicsUniversity of Adelaide, South Australia
P. R. Scott
Affiliation:
Department of Pure MathematicsUniversity of Adelaide, South Australia
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Abstract

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The isoperimetric problem in the Euclidean plane is completely solved for bounded, convex sets which are symmetric about the origin, and which contain no non-zero point of the integral lattice.

MSC classification

Secondary: 52A40: Inequalities and extremum problems 52A10: Convex sets in $2$ dimensions (including convex curves)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1979 , pp. 27 - 36
Copyright
Copyright © Australian Mathematical Society 1979

References

Besicovitch, A. S. (1952), ‘Variants of a classical isoperimetric problem’, Quart. J. Math. Oxford (2) 3, 42–49.CrossRefGoogle Scholar
Eggleston, H. G. (1963), Convexity (Cambridge Tract 47).Google Scholar
Minkowski, H. (1896), Geometrie der Zahlen (Leipzig and Berlin).Google Scholar
Scott, P. R. (1974), ‘An area-perimeter problem’, Amer. Math. Monthly 81 (8), 884–885.CrossRefGoogle Scholar