最大角平分法
The largest angle bisection procedure
摘要：
{ \it最大角平分}过程是通过构造$T$的最大角的角平分线将给定三角形$T$分割成两个较小三角形的操作。将该过程应用于这两个三角形中的每一个三角形，产生将$T$划分为四个较小三角形的分区。以这种方式继续，在$n$迭代之后，初始三角形被划分为$2^n$小三角形。我们证明了当$n$趋于无穷大时，所有这些$2^n$三角形的直径都趋于$0$，所有这些三角形的最小角都有界远离$0$，并且除了$T$是等腰直角三角形之外，相异三角形的个数是无界的.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
