Machin-like formulae
M000000428
$$\pi=24\arctan\left(\frac{1}{10}\right)+12\arctan\left(\frac{1}{18}\right)+8\arctan\left(\frac{1}{100}\right)+8\arctan\left(\frac{1}{307}\right)-12\arctan\left(\frac{1}{515}\right)+8\arctan\left(\frac{1}{9901}\right)$$
Compact formula
24[10] + 12[18] + 8[100] + 8[307] - 12[515] + 8[9901]
Lehmer's measure
3.31773
References
Castellanos, Dario. The ubuquitous π,
Mathematics Magazine
61, 1988. [DOI:
10.1080/0025570X.1988.11977350
]
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