Machin-like formula

In mathematics, Machin-like formulas are a class of identities involving π = 3.14159... They have the form

Related Topics:
Mathematics - π

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:rac{pi}{4} = sum_{n}^N a_n rctanrac{1}{b_n}

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with a_n and b_n integers. These formulas generalize John Machin's formula from 1706,

Related Topics:
Integer - John Machin - 1706

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:rac{pi}{4} = 4 rctanrac{1}{5} - rctanrac{1}{239},

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which he used along with the Taylor series expansion of arctan to compute π to 100 decimal places. Indeed, the same method is still among the most efficient known for computing large amounts of digits of π with digital computers.

Related Topics:
Taylor series - Arctan - Computer

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