Machin-like formulae

M000108

$$\pi=6348\arctan\left(\frac{1}{2852}\right)+1180\arctan\left(\frac{1}{4193}\right)+2372\arctan\left(\frac{1}{4246}\right)+1436\arctan\left(\frac{1}{39307}\right)+1924\arctan\left(\frac{1}{55603}\right)+2500\arctan\left(\frac{1}{211050}\right)-2832\arctan\left(\frac{1}{390112}\right)$$
Compact formula6348[2852] + 1180[4193] + 2372[4246] + 1436[39307] + 1924[55603] + 2500[211050] - 2832[390112]
Lehmer's measure1.63617
NotesThis formula was used in 2024 by Matt Parker and a large group of volunteers to compute 139 digits of π.
References
Arndt (1993) (full reference coming soon)

Arndt, Jörg and Harnel, Christoph. Pi - Unleashed, 1998. [DOI: 10.1007/978-3-642-56735-3]

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