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.


Pages in category "Pi with Machin's formula"

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