Machin-like formulae
M000372
$$\pi=16\arctan\left(\frac{1}{5}\right)-4\arctan\left(\frac{1}{226}\right)+4\arctan\left(\frac{1}{4155}\right)$$
Compact formula
16[5] - 4[226] + 4[4155]
Lehmer's measure
2.13181
References
STØRMER (1896)
(full reference coming soon)