三角形、分形和意大利面
Triangles, Fractales and Spaghetti
摘要：
有一个著名的几何概率问题，可以引用为破碎的意大利面条问题。它解决了以下问题：一根意大利面条分成三部分，并且所有的点都有相同的概率成为断裂点。三根棍子放在一起形成三角形的概率是多少？在这些笔记中，我们描述了隐藏在这个问题的对称版本背后的几何模式，即参数化这个问题的样本空间的分形。利用该分形，我们解决了关于获得$δ$ -等边三角形的概率的问题。
英文摘要：
There is well-known problem of geometric probability which can be quote as the Broken Spaghetti Problem. It addresses the following question: A stick of spaghetti breaks into three parts and all points of the stick have the same probability to be a breaking point. What is the probability that the three sticks, putting together, form a triangle? In these notes, we describe a hidden geometric pattern behind the symmetric version of this problem, namely a fractal that parametrizes the sample space of this problem. Using that fractal, we address the question about the probability to obtain a $δ$-equilateral triangle.
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。
