Machin’s Pi

1706 John Machin developed a formula for calculating Pi to an arbitrary number of decimal places:

\boxed{\displaystyle \pi = \text {4 [4.arccot(5) - arccot(239)]} }

\boxed {\displaystyle \text{arccot (x)} = \frac{1}{x} - \frac {1}{3{x^{3}}} + \frac {1}{5{x^{5}}}-\frac {1}{7{x^{7}}} + \cdots }

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