Web Reference: 求真书院2026Pi节挑战赛即将开启!求真书院Pi节挑战赛将于3月15日举办。 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!
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