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arXiv · 1908.02749

The largest angle bisection procedure

Dan Ismailescu·Joehyun Kim·Kelvin Kim·Jeewoo Lee
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Abstract

The {\it largest angle bisection} procedure is the operation which partitions a given triangle, $T$, into two smaller triangles by constructing the angle bisector of the largest angle of $T$. Applying the procedure to each of these two triangles produces a partition of $T$ into four smaller triangles. Continuing in this manner, after $n$ iterations, the initial triangle is divided into $2^n$ small triangles. We prove that as $n$ approaches infinity, the diameters of all these $2^n$ triangles tend to $0$, the smallest angle of all these triangles is bounded away from $0$, and that, with the exception of $T$ being an isosceles right triangle, the number of dissimilar triangles is unbounded.

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Dan Ismailescu, Joehyun Kim, Kelvin Kim, Jeewoo Lee. 2019-08-06. The largest angle bisection procedure. https://arxiv.org/abs/1908.02749

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