论文标题
用$π$ - 承诺的角度的细分三角形
Subdividing triangles with $π$-commensurable angles
论文作者
论文摘要
平面三角形的内部点确定了一个细分为六个子三角形。具有与$π$相称的角度的三角形称为$π$ - 可以承诺。对于这样的三角形，每个子三角形都是$π$ - 可承受的。我们证明，除了角度双压提供的一个$π$ - $允许的分区外，有许多$π$ - 承认的三角形。我们计算三角形的$π$ - 可承受的细分数。我们也对z学位三角形的z程度细分进行了类似的计数。最后，我们表明，在递归分区中，按角度分类是必不可少的，因为任何$π$可承受的三角形的递归$π$ - $π$可承受的细分最终都涉及角度划分的细分。
A point in the interior of a planar triangle determines a subdivision into six subtriangles. A triangle with angles commensurable with $π$ is called $π$-commensurable. For such a triangle a subdivision where each of the subtriangles are $π$-commensurable too is called $π$-commensurable. We prove that there are infinitely many $π$-commensurable triangles that do not admit any $π$-commensurable subdivision except the one given by angle bisectors. We count the number of $π$-commensurable subdivisions of triangles. We perform a similar count for Z-degree sub-divisions of Z-degree triangles too. Finally we show that subdivision by angle bisectors is essential in recursive subdivisions in the sense that recursive $π$-commensurable subdivisions of any $π$-commensurable triangle ultimately involve a subdivision by angle bisectors.
