论文标题
伯特兰在监视器上的悖论
Bertrand's paradox on a monitor
论文作者
论文摘要
我们通过离散的几何形状和老式但可靠的离散概率来研究Bertrand的概率悖论。我们以$ 1/n $ tims $ 1/n $ box的价格近似平面单位圆圈，并计算距离距离$ \ sqrt {3} $的盒子对。对于$ n \至\ infty $，此类对的比例为$ \ frac {1+ \ sqrt {3}}} {8} {8} - \ frac {π（2- \ sqrt {3}}} {96} {96} = 0.33273 \ dots \ dots \ dots \;。 $$
We investigate Bertrand's probabilistic paradox through the lens of discrete geometry and old-fashioned but reliable discrete probability. We approximate the plane unit circle with $1/n$ times $1/n$ boxes and count the pairs of boxes separated by distance more than $\sqrt{3}$. For $n\to\infty$ the proportion of such pairs goes to $$ \frac{1+\sqrt{3}}{8}-\frac{π(2-\sqrt{3})}{96}=0.33273\dots\;. $$
