Machin-like formulae
M000396
$$\pi=16\arctan\left(\frac{1}{5}\right)-4\arctan\left(\frac{1}{70}\right)+4\arctan\left(\frac{1}{99}\right)$$
Compact formula
16[5] - 4[70] + 4[99]
Lehmer's measure
2.47374
References
EULER (1738 or earlier - published 1744)
(full reference coming soon)