Web Reference: Archimedes pi (图片来源: Wikipedia) 可以看出，到了正八边形时，内接八边形与外切八边形之间的“间隙”比正方形的情况小了。此时 π 的估算值相对于正方形的情况会有一个精度上的提升。但是，现在的问题是：八边形的周长如何计算？而且就算把八边形的周长计算出来了，那16边形、32边形岂不是精度 ... 令 s=4 ，又得到了一种新的计算 \pi 的方法： \frac {\pi^4} {90}=\sum_ {n=1}^\infty\frac {1} {n^4}=1+\frac {1} {2^4}+\frac {1} {3^4}+\cdots, 收敛速度相对来说还是比较快的，仅需 \color {red} {5} 项便可精确到 3.14 。 方案五：Ramanujan 表示，你们全是弟弟！ 1π=∑n=0+∞(6n)!(3n)!(n!)3⋅A+BnC3n⋅−C3 \frac{1}{\pi}=\sum_{n=0}^{+\infty} \frac{(6 n) !}{(3 n) !(n !)^3} \cdot \frac{{\color{red}A}+{\color{green}B}n ...
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