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An isodiametric problem with lattice-point constraints

Published online by Cambridge University Press:  17 April 2009

M. A. Hernández Cifre  and
P.R. Scott
M. A. Hernández Cifre
Affiliation:
Departamento de MatemáticasUniversidad de Murcia30100-MurciaSpain e-mail: mhcifre@fcu.um.es
P.R. Scott
Affiliation:
Department of Pure MathematicsUniversity of AdelaideSouth Australia 5005Australia e-mail: pscott@maths.adelaide.edu.au
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Abstract

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The isodiametric problem in the Euclidean plane is solved for bounded convex sets, which are symmetric about the origin, and which contain no interior non-zero point of an arbitrary lattice L.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 289 - 294
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Fedorov, E.S., ‘Elements of the study of figures’, Zap. Mineral. Imper. S. Petersburgskogo Obsc. 21 (1885), 1–279; Izdat Akad Nauk SSSR Moscow (1953).Google Scholar
[2]Minkowski, H., Geometrie der Zahlen (Leipzig, Berlin, 1896 and 1910; Chelsea, New York 1953).Google Scholar
[3]Scott, P.R. and Arkinstall, J., ‘An isoperimetric problem with lattice point constraints’, J. Austral. Math. Soc. 27 (1979), 27–36.Google Scholar