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Circumradius-diameter and width-inradius relations for lattice constrained convex sets

Published online by Cambridge University Press:  17 April 2009

Poh Wah Awyong  and
Paul R. Scott
Poh Wah Awyong
Affiliation:
Division of Mathematics, National Institute of Education, 469 Bukit Timah Road, Singapore 259756 e-mail: awyongpw@nievax.nie.ac.sg
Paul R. Scott
Affiliation:
Department of Pure Mathematics, The University of Adelaide, South Australia 5005 e-mail: pscott@maths.adelaide.edu.au
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Abstract

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Let K be a planar, compact, convex set with circumradius R, diameter d, width w and inradius r, and containing no points of the integer lattice. We generalise inequalities concerning the ‘dual’ quantities (2R − d) and (w − 2r) to rectangular lattices. We then use these results to obtain corresponding inequalities for a planar convex set with two interior lattice points. Finally, we conjecture corresponding results for sets containing one interior lattice point.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 147 - 152
Copyright
Copyright © Australian Mathematical Society 1999

References

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