The enhancement of Machin’s formula by Todd’s process
The enhancement of Machin’s formula by Todd’s process
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托德工艺对机器配方的增强
DOI：
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发表时间：
1996
影响因子：
0.3
通讯作者：
Michael R. Wetherfield
中科院分区：
文献类型：
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作者：
Michael R. Wetherfield
1. 从17世纪末到20世纪80年代，大多数π值的近似值都使用格列高利级数：它收敛于-1和+1之间的tanθ值。由于这类级数最简单，收敛速度也最慢，写成x = cotθ，这个级数就变成了π/4的表达式被设计出来，它包含了更大的数的反切线，使得这个级数收敛得更快；在这些表达式（这里称为“恒等式”）中，最著名的可能是“Machin公式”：
1. Background From the end of the 17th century until the 1980s, most approximations to the value of π made use of Gregory’s series: which converges for values of tanθ between -1 and +1. Since , the simplest, and most slowly convergent, series of this kind is Writing x = cotθ, the series becomes Expressions for π/4 have been devised which involve the inverse cotangents of larger numbers, causing the series to converge much faster; of such expressions (referred to herein as ‘identities’) probably the most celebrated is ‘Machin’s Formula’: