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Results 1 - 10
of
101
by congruent triangles
, 2001
"... Abstract. We give a new classification of tilings of the 2-dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure poin ..."
Abstract
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Abstract. We give a new classification of tilings of the 2-dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure
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
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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
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 ..."
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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
Classification of tilings of the 2-dimensional sphere by congruent triangles
- Hiroshima Math. J
, 2002
"... We give a new classification of tilings of the 2-dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure points, give a ..."
Abstract
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Cited by 16 (0 self)
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We give a new classification of tilings of the 2-dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure points, give
Icosahedra constructed from congruent triangles, Grünmbaum birthday issue
- Discrete Comput. Geometry
"... Dedicated to Branko Grünbaum on the occasion of his seventieth birthday. It is possible to construct a figure in 3 dimensions which is combinatorially equivalent to a regular icosahedron, and whose faces are all congruent but not equilateral. Such icosamonohedra can be convex or nonconvex, and can b ..."
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Cited by 2 (0 self)
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Dedicated to Branko Grünbaum on the occasion of his seventieth birthday. It is possible to construct a figure in 3 dimensions which is combinatorially equivalent to a regular icosahedron, and whose faces are all congruent but not equilateral. Such icosamonohedra can be convex or nonconvex, and can
The maximum number of empty congruent triangles determined by a point set, Revue Roumaine de Math. Pures et Appliquées 50
, 2005
"... Let S be a set of n points in the plane and consider a family of (nondegenerate) pairwise congruent triangles whose vertices belong to S. While the number of such triangles can grow superlinearly in n — as it happens in lattice sections of the integer grid — it has been conjectured by Brass that the ..."
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Cited by 1 (1 self)
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Let S be a set of n points in the plane and consider a family of (nondegenerate) pairwise congruent triangles whose vertices belong to S. While the number of such triangles can grow superlinearly in n — as it happens in lattice sections of the integer grid — it has been conjectured by Brass
Circumcenters of Residual Triangles
"... Abstract. This paper is an extension of Mario Dalcı́n’s work on isotomic in-scribed triangles and their residuals [1]. Considering the circumcircles of resid-ual triangles with respect to isotomic inscribed triangles there are two congruent triangles of circumcenters. We show that there is a rotatio ..."
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Abstract. This paper is an extension of Mario Dalcı́n’s work on isotomic in-scribed triangles and their residuals [1]. Considering the circumcircles of resid-ual triangles with respect to isotomic inscribed triangles there are two congruent triangles of circumcenters. We show that there is a
THE CONGRUENT NUMBER PROBLEM
"... A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include Pythagorean triples like (3, 4, 5). We can scale such triples to get other rational right triangles, like (3/2, 2, 5/2). Of course, usually when two sides are ratio ..."
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A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include Pythagorean triples like (3, 4, 5). We can scale such triples to get other rational right triangles, like (3/2, 2, 5/2). Of course, usually when two sides
Results 1 - 10
of
101
