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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)

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