Machin-like formulae
M000400
$$\pi=20\arctan\left(\frac{1}{7}\right)+8\arctan\left(\frac{1}{18}\right)-8\arctan\left(\frac{1}{57}\right)$$
Compact formula
20[7] + 8[18] - 8[57]
Lehmer's measure
2.54945
References
STØRMER (1896)
(full reference coming soon)