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Isoperimetric problems for tilings

Published online by Cambridge University Press:  26 February 2010

L. Fejes Tóth
L. Fejes Tóth
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1053 Budapest, Hungary.
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Extract

We consider a tiling of a square with convex tiles of areas a1,… aN and perimeters p1,…,pN and pose the following problems.

PROBLEM 1. For given values of a1, …, aN find the minimum of P = p1 + … + pN.

PROBLEM 2. For given values of p1,…,pN find the maximum of A = a1+…+aN.

Type
Research Article
Information
Mathematika , Volume 32 , Issue 1 , June 1985 , pp. 10 - 15
Copyright
Copyright © University College London 1985

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References

1.Bambah, R. P. and Rogers, C. A.. Covering the plane with convex sets. J. London Math. Soc., 27 (1952), 304–314.Google Scholar
2.Fejes Tóth, G.. An isoperimetric problem for tessellations. Studia Sci. Math. Hungar., 10 (1975), 171–173.Google Scholar
3.Fejes Tóth, L.. Regular Figures (Pergamon Press, 1964).Google Scholar