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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 D be an arbitrary triangle with minimum angle a. Let D 0 be any triangle generated in the iterated application of the longest-edge trisection. Let… (More)

In this note, by using complex variable functions, we present a new simpler proof of the degeneracy property of the longest-edge n-section of triangles for n P 4. This means that the longest-edge n-section of triangles for n P 4 produces a sequence of triangles with minimum interior angle converging to zero. Unstructured mesh generation and adaptive mesh… (More)

The Longest-Edge (LE) trisection of a triangle is obtained by joining the two points which divide the longest edge in three with the opposite vertex. If LE-trisection is iteratively applied to an initial triangle, then the maximum diameter of the resulting triangles is between two sharpened decreasing functions. This paper mathematically answers the… (More)

Islands), who passed away on July 11, 2012. Prof. González Vera was a recognized specialist in Approximation Theory , Orthogonal Polynomials and Quadrature Formulae, and was author of more than one hundred fifty papers published in prestigious international journals in the area of Applied Mathematics. He also wrote several books, among which specially… (More)

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