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New inequalities for planar convex sets with lattice point constraints

Published online by Cambridge University Press:  17 April 2009

Poh W. Awyong  and
Paul R. Scott
Poh W. Awyong
Affiliation:
Department of Pure Mathematics, The University of Adelaide, South Australia 5005, e-mail: pawyong@maths.adelaide.edu.au, pscott@maths.adelaide.edua.au
Paul R. Scott
Affiliation:
Department of Pure Mathematics, The University of Adelaide, South Australia 5005, e-mail: pawyong@maths.adelaide.edu.au, pscott@maths.adelaide.edua.au
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Abstract

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We obtain new inequalities relating the inradius of a planar convex set with interior containing no point of the integral lattice, with the area, perimeter and diameter of the set. By considering a special sublattice of the integral lattice, we also obtain an inequality concerning the inradius and area of a planar convex set with interior containing exactly one point of the integral lattice.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 391 - 396
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Eggleston, H.G., Convexity (Cambridge University Press, Cambridge, 1958).CrossRefGoogle Scholar
[2]Scott, P.R., ‘Two inequalities for convex sets with lattice point constraints in the plane’, Bull. London Math. Soc. 11 (1979), 273–278.CrossRefGoogle Scholar
[3]Scott, P.R., ‘Further inequalities for convex sets with lattice point constraints’, Bull. Austral. Math. Soc. 21 (1980), 7–12.CrossRefGoogle Scholar