Skip to main content Accessibility help

Isoperimetric problems for tilings

  • L. Fejes Tóth (a1)


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.



Hide All
1.Bambah, R. P. and Rogers, C. A.. Covering the plane with convex sets. J. London Math. Soc., 27 (1952), 304314.
2.Fejes Tóth, G.. An isoperimetric problem for tessellations. Studia Sci. Math. Hungar., 10 (1975), 171173.
3.Fejes Tóth, L.. Regular Figures (Pergamon Press, 1964).
MathJax is a JavaScript display engine for mathematics. For more information see


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed