Abstract
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 minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles.
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Perdomo, F., Plaza, Á. Properties of triangulations obtained by the longest-edge bisection. centr.eur.j.math. 12, 1796–1810 (2014). https://doi.org/10.2478/s11533-014-0448-4
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DOI: https://doi.org/10.2478/s11533-014-0448-4