Divisible tilings in the hyperbolic plane.
Broughton, S.Allen, Haney, Dawn M., McKeough, Lori T., Smith Mayfield, Brandy (2000)
The New York Journal of Mathematics [electronic only]
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Displaying similar documents to “Metric distorsion and triangle maps.”
Divisible tilings in the hyperbolic plane.
Characterizing the Delaunay decompositions of compact hyperbolic surfaces.
Leibon, Gregory (2002)
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Properties of triangulations obtained by the longest-edge bisection
Francisco Perdomo, Ángel Plaza (2014)
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The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the...
Hyperbolic Realizations of Tilings by Zhuk Simplices
Milica Stojanović (1997)
Matematički Vesnik
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Tilings of the sphere with right triangles. II: The , subfamily.
Dawson, Robert J. MacG., Doyle, Blair (2006)
The Electronic Journal of Combinatorics [electronic only]
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Andreev’s Theorem on hyperbolic polyhedra
Roland K.W. Roeder, John H. Hubbard, William D. Dunbar (2007)
Annales de l’institut Fourier
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In 1970, E.M.Andreev published a classification of all three-dimensional compact hyperbolic polyhedra (other than tetrahedra) having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, , Andreev’s Theorem provides five classes of linear inequalities, depending on , for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing with the assigned dihedral angles. Andreev’s Theorem also shows that...
Dihedral f-tilings of the sphere by equilateral and scalene triangles-I
A. M. D'Azevedo Breda, Patrícia S. Ribeiro, Altino F. Santos (2010)
Rendiconti del Seminario Matematico della Università di Padova
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Tilings of the sphere with right triangles. I: The asymptotically right families.
Dawson, Robert J. MacG., Doyle, Blair (2006)
The Electronic Journal of Combinatorics [electronic only]
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Circumcenter, Circumcircle and Centroid of a Triangle
Roland Coghetto (2016)
Formalized Mathematics
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We introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula...
Morley’s Trisector Theorem
Roland Coghetto (2015)
Formalized Mathematics
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Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Tilings of the sphere with right triangles. III: The asymptotically obtuse families.
Dawson, Robert J.Macg., Doyle, Blair (2007)
The Electronic Journal of Combinatorics [electronic only]
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