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arXiv · 2004.01034

Incongruent equipartitions of the plane into quadrangles of equal perimeter

Dirk Frettlöh·Christian Richter
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Abstract

Motivated by a question of R.\ Nandakumar, we show that the Euclidean plane can be dissected into mutually incongruent convex quadrangles of the same area and the same perimeter. As a byproduct we obtain vertex-to-vertex dissections of the plane by mutually incongruent triangles of unit area that are arbitrarily close to the periodic vertex-to-vertex tiling by equilateral triangles.

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Dirk Frettlöh, Christian Richter. 2020-04-01. Incongruent equipartitions of the plane into quadrangles of equal perimeter. https://arxiv.org/abs/2004.01034

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