Machin-like formulae
M000409
$$\pi=10\arctan\left(\frac{1}{3}\right)-4\arctan\left(\frac{1}{53}\right)-2\arctan\left(\frac{1}{4443}\right)$$
Compact formula
10[3] - 4[53] - 2[4443]
Lehmer's measure
2.95000
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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