Machin-like formulae
M000406
$$\pi=20\arctan\left(\frac{1}{5}\right)-12\arctan\left(\frac{1}{18}\right)-8\arctan\left(\frac{1}{57}\right)$$
Compact formula
20[5] - 12[18] - 8[57]
Lehmer's measure
2.79683
References
STØRMER (1896)
(full reference coming soon)