منابع مشابه
Tiling a Strip with Triangles
In this paper, we examine the tilings of a 2 × n “triangular strip” with triangles. These tilings have connections with Fibonacci numbers, Pell numbers, and other known sequences. We will derive several different recurrences, establish some properties of these numbers, and give a refined count for these tilings (i.e., by the number and type of triangles used) and establish several properties of...
متن کاملTiling Polygons with Lattice Triangles
Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinate of the vertices in any tiling are ratio...
متن کاملTiling a Triangle with Congruent Triangles
We investigate the problem of cutting a triangle ABC into N congruent triangles (the “tiles”), which may or may not be similar to ABC. We wish to characterize the numbers N for which some triangle ABC can be tiled by N tiles, or more generally to characterize the triples (N,T ) such that ABC can be N-tiled using tile T . In the first part of the paper we exhibit certain families of tilings whic...
متن کاملTiling the Unit Square with 5 Rational Triangles
We prove that there are 14 distinct ways to tile the unit square (modulo the symmetries of the square) with 5 triangles such that the 5-tiling is not a subdivision of a tiling using fewer triangles. We then demonstrate how to construct infinitely many rational tilings in each of the 14 configurations. This stands in contrast to a long standing inability to find rational 4-tilings of the unit sq...
متن کاملTiling triangle ABC with congruent triangles similar to ABC
We investigate the problem of cutting a triangle ABC into N congruent triangles (the “tiles”), each of which is similar to ABC. The more general problem when the tile is not similar to ABC is not treated in this paper; see [1]. We give a complete characterization of the numbers N for which some triangle ABC can be tiled by N tiles similar to ABC, and also a complete characterization of the numb...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/3478