Machin-like formulae
M000000305
$$\pi=48\arctan\left(\frac{1}{15}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{580}\right)-16\arctan\left(\frac{1}{1710}\right)$$
Compact formula
48[15] - 4[239] - 16[580] - 16[1710]
Lehmer's measure
1.94190
References
Castellanos, Dario. The ubuquitous π,
Mathematics Magazine
61, 1988. [DOI:
10.1080/0025570X.1988.11977350
]
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