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On the width of a planar convex set containing zero or one lattice points

Published online by Cambridge University Press:  17 April 2009

Paul R. Scott
Paul R. Scott
Affiliation:
Department of Mathematics, The University of Adelaide, Adelaide SA 5001, Australia
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We generalise to a rectangular lattice a known result about the maximal width of a planar compact convex set containing no points of the integral lattice. As a corollary we give a new short proof that the planar compact convex set of greatest width which contains just one point of the triangular lattice is an equilateral triangle.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 47 - 53
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Blaschke, W., Kreis und Kugel (W. de Gruyter, Berlin, 1956).CrossRefGoogle Scholar
[2]Scott, P.R., ‘A lattice problem in the plane’, Mathematika 20 (1973), 247–252.CrossRefGoogle Scholar
[3]Scott, P.R., ‘On planar convex sets containing one lattice point’, Quart. J. Math. Oxford Ser. 2 36 (1985), 105–111.CrossRefGoogle Scholar
[4]Scott, P.R., ‘Convex sets and the hexagonal lattice’, Math. Mag. 51 (1978), 237–238.CrossRefGoogle Scholar
[5]Wetwitschka, K., ‘Zur Breite konvexer Mengen mit einem inneren Gitterpunkt im triangularen Gitter’, Ann. Univ. Sci. Budapest 34 (1991), 121–135.Google Scholar