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Tiling the plane with noncongruent triangles

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Tiling the plane with noncongruent triangles
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21
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Nandakumar raised several interesting questions on plane tilings. Among them is the problem if the plane can be tiled with pairwise noncongruent triangles that are both equal area and equal perimeter. We prove that this is not possible and survey related results on plane tilings including relaxed versions of this problem. The results in the talk are joint with Andrey Kupavskii and Janos Pach.