|Title:||Proving the non-degeneracy of the longest-edge trisection by a space of triangular shapes with hyperbolic metric||Authors:||Perdomo, Francisco
|UNESCO Clasification:||120603 Análisis de errores||Keywords:||Finite element method
|Issue Date:||2013||Project:||Particiones Triangulares y Algoritmos de Refinamiento.||Journal:||Applied Mathematics and Computation||Abstract:||From an initial triangle, three triangles are obtained joining the two equally spaced points of the longest-edge with the opposite vertex. This construction is the base of the longest-edge trisection method. Let Δ be an arbitrary triangle with minimum angle α. Let Δ′ be any triangle generated in the iterated application of the longest-edge trisection. Let α′ be the minimum angle of Δ′. Thus α′≥α/c with c=π/3arctan3/11 is proved in this paper. A region of the complex half-plane, endowed with the Poincare hyperbolic metric, is used as the space of triangular shapes. The metric properties of the piecewise-smooth complex dynamic defined by the longest-edge trisection are studied. This allows us to obtain the value c.||URI:||http://hdl.handle.net/10553/51606||ISSN:||0096-3003||DOI:||10.1016/j.amc.2013.06.075||Source:||Applied Mathematics and Computation [ISSN 0096-3003], v. 221, p. 424-432|
|Appears in Collections:||Artículos|
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