Machin-like formulae
M000000235
$$\pi=48\arctan\left(\frac{1}{15}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{433}\right)+16\arctan\left(\frac{1}{1875333}\right)$$
Compact formula
48[15] - 4[239] - 16[433] + 16[1875333]
Lehmer's measure
1.80942
References
Castellanos, Dario. The ubuquitous π,
Mathematics Magazine
61, 1988. [DOI:
10.1080/0025570X.1988.11977350
]
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