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Noncongruent Equidissections of the Plane

  • D. Frettlöh
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 234)

Abstract

Nandakumar asked whether there is a tiling of the plane by pairwise non-congruent triangles of equal area and equal perimeter. Here a weaker result is obtained: there is a tiling of the plane by pairwise non-congruent triangles of equal area such that their perimeter is bounded by some common constant. Several variants of the problem are stated, some of them are answered.

Keywords

Tilings Equipartitions 

Notes

Acknowledgements

The author expresses his gratitude to R. Nandakumar for providing several interesting problems. Particular thanks to one of the anonymous referees for providing the “no” in Table 1 and for other valuable remarks. Special thanks to Jens Schubert for helpful discussions on this topic during a pleasant summer weekend in Bochum.

References

  1. 1.
    H.T. Croft, K.J. Falconer, R.K. Guy, Unsolved Problems in Geometry (Springer, New York, 1991)Google Scholar
  2. 2.
    B. Grünbaum, G.C. Shephard, Tilings and Patterns (W.H. Freeman, New York, 1987)Google Scholar
  3. 3.
    R. Nandakumar, http://nandacumar.blogspot.in, post from Dec 2014 and Jan 2015
  4. 4.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Bielefeld UniversityBielefeldGermany

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