与一根断了的棍子有关的事情
Things to do with a broken stick
摘要：
我们使用断棒问题（可以追溯到庞加莱）的思想，计算三个断裂部分是：三角形中的中线，高度，外圆半径，角平分线，从I或O到顶点的距离，分别是边，以及三角形中确定（或多或少唯一）三角形的其他三个元素的相应概率。对于每一种情况，我们也看概率，三角形是（或多或少唯一）定义的元素，是尖锐的，并比较是钝角。
英文摘要：
We use the idea of the broken stick problem (which goes back to Poincare) and calculate the corresponding probabilities for the cases in which the three broken part are: the medians in a triangle, the altitudes, radii of excircles, angle bisectors, distances from I or O to the vertices, respectively sides, and some other three elements in a triangle which determine (more or less uniquely) the triangle. For each case we also look at the probability that the triangle that is (more or less uniquely) defined by the elements, being acute and compare to that of being obtuse.
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。
