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A lattice problem in the plane

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

P. R. Scott
P. R. Scott
Affiliation:
Department of Mathematics, University of Adelaide, Adelaide, South Australia.
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Extract

In [2], Sawyer considers a closed, central, convex region K which is such that, however it is displaced in the plane, a point of the integral lattice is covered. He shows that the area A(K) of K satisfies . We prove here a result in the opposite direction.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 20 , Issue 2 , December 1973 , pp. 247 - 252
Copyright
Copyright © University College London 1973

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References

1. Blaschke, W., Kreis und Kugel (W. de Gruyter, Berlin, 1956).Google Scholar
2. Sawyer, D. B., “On the covering of lattice points by convex regions”, Quart. J. Math. Oxford (2), 4 (1953), 284–292.CrossRefGoogle Scholar