Machin-like formulae
M000000234
$$\pi=244\arctan\left(\frac{1}{72}\right)-340\arctan\left(\frac{1}{1483}\right)-116\arctan\left(\frac{1}{8307}\right)-28\arctan\left(\frac{1}{9932}\right)+116\arctan\left(\frac{1}{27493}\right)-156\arctan\left(\frac{1}{29718}\right)$$
Compact formula
244[72] - 340[1483] - 116[8307] - 28[9932] + 116[27493] - 156[29718]
Lehmer's measure
1.80790
References
Chien-Lih, Hwang. More Machin-type identities,
The Mathematical Gazette
81(490), 120–121, 1997. [DOI:
10.2307/3618793
]
Download references as BibTeΧ