M000000059

$$\pi=176\arctan\left(\frac{1}{57}\right)+28\arctan\left(\frac{1}{239}\right)-48\arctan\left(\frac{1}{682}\right)+96\arctan\left(\frac{1}{12943}\right)$$

Compact formula	`176[57] + 28[239] - 48[682] + 96[12943]`
Lehmer's measure	1.58604
Notes	In 2022, this formula was used alongside M000213 to compute 1,241,100,000,000 decimal places of π.
References	Størmer, Carl. Solution complète en nombres entiers m, n, x, y et k de l'équation marctang(1/x) + narctang(1/y) = kπ/4, chapter 11 in Skrifter udgivne af Vidensakbsselskabet i Christiania I. Mathematisk-naturvidenskabelig klasse, 11.1–11.21, 1896. Download references as BibTeΧ