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Some inequalities for planar convex sets containing one lattice point

Published online by Cambridge University Press:  17 April 2009

M. A. Hernández Cifre  and
S. Segura Gomis
M. A. Hernández Cifre
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, 30100–Murcia, Spain e-mail: mhcifre@fcu.um.es, salsegom@fcu.um.es
S. Segura Gomis
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, 30100–Murcia, Spain e-mail: mhcifre@fcu.um.es, salsegom@fcu.um.es
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Abstract

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We obtain two inequalities relating the diameter and the (minimal) width with the area of a planar convex set containing exactly one point of the integer lattice in its interior. They are best possible. We then use these results to obtain some related inequalities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 159 - 166
Copyright
Copyright © Australian Mathematical Society 1998

References

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