Machin-like formulae
M000000222: Gauss's identity
$$\pi=48\arctan\left(\frac{1}{18}\right)+32\arctan\left(\frac{1}{57}\right)-20\arctan\left(\frac{1}{239}\right)$$
Name
Gauss's identity
Compact formula
48[18] + 32[57] - 20[239]
Lehmer's measure
1.78660
References
Gauss, Carl Friedrich. Werke volume 2, 1863.
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