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210
Noncongruence subgroups in H(2)
 INTERNAT. MATH. RES. NOTICES
, 2004
"... We study the congruence problem for subgroups of the modular group that appear as Veech groups of squaretiled surfaces in the minimal stratum of abelian differentials of genus two. ..."
Abstract

Cited by 7 (3 self)
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We study the congruence problem for subgroups of the modular group that appear as Veech groups of squaretiled surfaces in the minimal stratum of abelian differentials of genus two.
Algorithmic selfassembly of DNA Sierpinski triangles
 PLoS Biology
"... Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular selfassembly. Here we report the molecular realization, using twodimensional selfassembly of DNA tiles, of a cellular automat ..."
Abstract

Cited by 153 (13 self)
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automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern—a Sierpinski triangle—as it grows. To achieve this, abstract tiles were translated into DNA tiles based on doublecrossover motifs. Serving as input for the computation, long singlestranded DNA molecules were
Tiling a Triangle with Congruent Triangles
, 2010
"... 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 ..."
Abstract

Cited by 2 (2 self)
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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
DDG OF TRIANGLE TILES 1
, 2006
"... Discrete differential geometry of triangle tiles and algebra of closed trajectories ..."
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Discrete differential geometry of triangle tiles and algebra of closed trajectories
Tiling polygons with lattice triangles
, 2009
"... Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the xaxis, 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 ..."
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Cited by 1 (1 self)
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Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the xaxis, 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
Tiling a strip with triangles
"... Abstract In this paper, we introduce the tilings of a 2×n "triangular strip" with triangles. These tilings have connections with Fibonacci numbers, Pell numbers, and other known sequences. We derive several different recurrences, establish some properties of these numbers, and give a refi ..."
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Abstract In this paper, we introduce the tilings of a 2×n "triangular strip" with triangles. These tilings have connections with Fibonacci numbers, Pell numbers, and other known sequences. We derive several different recurrences, establish some properties of these numbers, and give a
TILINGS OF PARALLELOGRAMS WITH SIMILAR TRIANGLES
"... Abstract. We say that a triangle ∆ tiles the polygon P if P can be decomposed into finitely many nonoverlapping triangles similar to ∆. Let P be a parallelogram with angles δ and pi − δ (0 < δ ≤ pi/2) and let ∆ be a triangle with angles α, β, γ (α ≤ β ≤ γ). We prove that if ∆ tiles P then either ..."
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Abstract. We say that a triangle ∆ tiles the polygon P if P can be decomposed into finitely many nonoverlapping triangles similar to ∆. Let P be a parallelogram with angles δ and pi − δ (0 < δ ≤ pi/2) and let ∆ be a triangle with angles α, β, γ (α ≤ β ≤ γ). We prove that if ∆ tiles P
Further Triangle tilings
"... Here we give a more complete reckoning of the conjecture discussed in “Regular Production Systems and Triangle Tilings ” [16] Here we discuss which triangles do, and which don’t, admit a tiling of H 2, E 2, and S 2. These notes are meant to pick up as “Regular Production Systems and Triangle Tilings ..."
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Here we give a more complete reckoning of the conjecture discussed in “Regular Production Systems and Triangle Tilings ” [16] Here we discuss which triangles do, and which don’t, admit a tiling of H 2, E 2, and S 2. These notes are meant to pick up as “Regular Production Systems and Triangle
Tiling triangle ABC with congruent triangles similar to ABC
, 2010
"... 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 tria ..."
Abstract
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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
Results 1  10
of
210