Category:Pi with Machin's formula

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[edit] Machin's formula

A simple way to compute the mathematical constant π ≈ 3.14159 with any desired precision is due to John Machin. In 1706, he found the formula

\frac{\pi}{4} = 4 \, \arccot \,5 - \arccot \,239

which he used along with the Taylor series expansion of the arc cotangent function,

\arccot x = \frac{1}{x} - \frac{1}{3 x^3} + \frac{1}{5 x^5} - \frac{1}{7 x^7} + \dots

to calculate 100 decimals by hand. The formula is well suited for computer implementation, both to compute π with little coding effort (adding up the series term by term) and using more advanced strategies (such as binary splitting) for better speed.

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Pages in category "Pi with Machin's formula"

The following 5 pages are in this category, out of 5 total.