Tilings of the plane with unit area triangles of bounded diameter
نویسندگان
چکیده
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.
منابع مشابه
Tilings with noncongruent triangles
We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that no convex polygon with more than three sides can be tiled with finitely many triangles such that no pair of them share a full side.
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عنوان ژورنال:
- CoRR
دوره abs/1712.03118 شماره
صفحات -
تاریخ انتشار 2017