Machin-like formulae
M000000307
$$\pi=32\arctan\left(\frac{1}{10}\right)-4\arctan\left(\frac{1}{239}\right)-32\arctan\left(\frac{1}{1020}\right)+16\arctan\left(\frac{1}{52525}\right)$$
Compact formula
32[10] - 4[239] - 32[1020] + 16[52525]
Lehmer's measure
1.96467
References
Castellanos, Dario. The ubuquitous π,
Mathematics Magazine
61, 1988. [DOI:
10.1080/0025570X.1988.11977350
]
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