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Inradius and circumradius for planar convex bodies containing no lattice points

Published online by Cambridge University Press:  17 April 2009

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

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Let K be a planar convex body containing no points of the integer lattice. We give a new inequality relating the inradius and circumradius of K.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 163 - 168
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Awyong, P.W., ‘An inequality relating the circumradius and diameter of two-dimensional lattice-point-free convex bodies’, Amer. Math. Monthly (to appear).Google Scholar
[2]Awyong, P.W. and Scott, P.R., ‘New inequalities for planar convex sets with lattice point constraints’, Bull. Austral. Math. Soc. 54 (1996), 391–396.CrossRefGoogle Scholar
[3]Eggleston, H.G., Convexity, Cambridge Tracts in Mathematics and Mathematical Physics 47 (Cambridge University Press, New York, 1958).CrossRefGoogle Scholar
[4]Scott, P.R., ‘A lattice problem in the plane’, Mathematika 20 (1973), 247–252.CrossRefGoogle Scholar
[5]Scott, P.R., ‘Two inequalities for convex sets with lattice point constraints in the plane’, Bull. London. Soc. 11 (1979), 273–278.CrossRefGoogle Scholar
[6]Scott, P.R., ‘Further inequalities for convex sets with lattice point constraints in the plane’, Bull. Austral. Math. Soc. 21 (1980), 7–12.CrossRefGoogle Scholar