Machin-like formulae
M000336
$$\pi=20\arctan\left(\frac{1}{7}\right)+16\arctan\left(\frac{1}{53}\right)+8\arctan\left(\frac{1}{4443}\right)$$
Compact formula
20[7] + 16[53] + 8[4443]
Lehmer's measure
2.03739
References
Wrench Jr., J. W. On the derivation of arctangent equalities,
The American Mathematical Monthly
45, 108–109, 1938. [DOI:
10.2307/2304280
]
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