Tilings of the plane with unit area triangles of bounded diameter

Andrey Kupavskii; G\'abor Tardos; J\'anos Pach

arxiv: 1712.03118 · v2 · pith:33374KZ5new · submitted 2017-12-08 · 🧮 math.CO · cs.DM· math.MG

Tilings of the plane with unit area triangles of bounded diameter

Andrey Kupavskii , J\'anos Pach , G\'abor Tardos This is my paper

classification 🧮 math.CO cs.DMmath.MG

keywords boundedtilingstrianglesareaequalexistperimeterplane

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There exist tilings of the plane with pairwise noncongruent triangles of equal area and bounded perimeter. Analogously, there exist tilings with triangles of equal perimeter, the areas of which are bounded from below by a positive constant. This solves a problem of Nandakumar.

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Tilings of the plane with unit area triangles of bounded diameter

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