Machin-like formulae
M000000381
$$\pi=48\arctan\left(\frac{1}{18}\right)+12\arctan\left(\frac{1}{70}\right)+20\arctan\left(\frac{1}{99}\right)+32\arctan\left(\frac{1}{307}\right)$$
Compact formula
48[18] + 12[70] + 20[99] + 32[307]
Lehmer's measure
2.24177
References
Bennett, A. A. Two new arctangent relations for π,
The American Mathematical Monthly
32(5), 253–255, 1925. [DOI:
10.2307/2299198
]
Download references as BibTeΧ