M000000382

$$\pi=640\arctan\left(\frac{1}{200}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{515}\right)-32\arctan\left(\frac{1}{4030}\right)-64\arctan\left(\frac{1}{50105}\right)-64\arctan\left(\frac{1}{62575}\right)-128\arctan\left(\frac{1}{500150}\right)-320\arctan\left(\frac{1}{4000300}\right)$$

Compact formula	`640[200] - 4[239] - 16[515] - 32[4030] - 64[50105] - 64[62575] - 128[500150] - 320[4000300]`
Lehmer's measure	2.24936
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