论文标题
$ e $和$π$之间的关系：Nilakantha的系列和Stirling的公式
Relations between $e$ and $π$: Nilakantha's series and Stirling's formula
论文作者
论文摘要
审查了$ e $和$π$之间的近似关系，建立了一些新的连接。 Nilakantha的$π$系列扩展是为了加速其收敛性的。它与$ e $的标准逆因素扩展进行了比较，以表现出几个第一期的相似性。此比较阐明了近似巧合$ e+2π\ 9 $的起源。使用Stirling的系列使我们能够说明关系$π^4+π^5 \ of e^6 $和$π^{9}/e^{8} \大约10 $。
Approximate relations between $e$ and $π$ are reviewed, some new connections being established. Nilakantha's series expansion for $π$ is transformed to accelerate its convergence. Its comparison with the standard inverse-factorial expansion for $e$ is performed to demonstrate similarity in several first terms. This comparison clarifies the origin of the approximate coincidence $e+2π\approx 9$. Using Stirling's series enables us to illustrate the relations $π^4+π^5 \approx e^6$ and $π^{9}/e^{8} \approx 10$.The role of Archimede's approximation $π=22/7$ is discussed.
