Machin-like formulae
M000000405
$$\pi=12\arctan\left(\frac{1}{4}\right)+4\arctan\left(\frac{1}{20}\right)+4\arctan\left(\frac{1}{1985}\right)$$
Compact formula
12[4] + 4[20] + 4[1985]
Lehmer's measure
2.73282
References
Machin, John. Unpublished paper submitted to the Royal Society, 1706.
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