论文标题
数学杂志问题2065年纯粹的3-D几何解决方案
A purely 3-D geometrical solution to Mathematics Magazine Problem 2065
论文作者
论文摘要
我们为数学杂志问题2065提出了一个纯粹的3-D几何解决方案。令$ \ mathcal {q} $是以$ \ mathbb {r}^3 $起源为中心的立方体。选择一个单位矢量$（a，b，c）$在单位球的表面上随机均匀地选择$ a^2+b^2+c^2 = 1 $，然后让$π$为平面$ ax+ax by by+cz = 0 $ yagin and the Origin，并正常为$（a，b，c）$。 $π$与$ \ Mathcal {q} $的相交的概率是什么？
We proposed a purely 3-D geometrical solution to Mathematics Magazine Problem 2065. Let $\mathcal{Q}$ be a cube centered at the origin of $\mathbb{R}^3$. Choose a unit vector $(a,b,c)$ uniformly at random on the surface of the unit sphere $a^2+b^2+c^2=1$, and let $Π$ be the plane $ax+by+cz=0$ through the origin and normal to $(a,b,c)$. What is the probability that the intersection of $Π$ with $\mathcal{Q}$ is a hexagon?
