Machin-like formulae
M000000369
$$\pi=48\arctan\left(\frac{1}{18}\right)+32\arctan\left(\frac{1}{99}\right)+12\arctan\left(\frac{1}{239}\right)+32\arctan\left(\frac{1}{307}\right)$$
Compact formula
48[18] + 32[99] + 12[239] + 32[307]
Lehmer's measure
2.12025
References
Lehmer, D. H. On Arccotangent Relations for π,
The American Mathematical Monthly
45(10), 657–664, 1938. [DOI:
10.1080/00029890.1938.11990873
]
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