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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Let ψ denote the square root of the golden ratio, ψ = √
متن کاملDNA triangles and self-assembled hexagonal tilings.
We have designed and constructed DNA complexes in the form of triangles. We have created hexagonal planar tilings from these triangles via self-assembly. Unlike previously reported structures self-assembled from DNA, our structures appear to involve bending of double helices. Bending helices may be a useful design option in the creation of self-assembled DNA structures. It has been suggested th...
متن کاملTilings with trichromatic colored-edges triangles
This paper studies the tilings with colored-edges triangles constructed on a triangulation of a simply connected orientable surface such that the degree of each interior vertex is even (such as, for (fundamental) example, a part of the triangular lattice of the plane). The constraints are that we only use three colors, all the colors appear in each tile and two tile can share an edge only if th...
متن کاملUnilateral and equitransitive tilings by equilateral triangles
A tiling of the plane by polygons is unilateral if each edge of the tiling is a side of at most one polygon of the tiling. A tiling is equitransitive if for any two congruent tiles in the tiling, there exists a symmetry of the tiling mapping one to the other. It is known that a unilateral and equitransitive (UE) tiling can be made with any finite number of congruence classes of squares. This ar...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0176-5