M000000001: Machin's formula

$$\pi=16\arctan\left(\frac{1}{5}\right)-4\arctan\left(\frac{1}{239}\right)$$
NameMachin's formula
Compact formula16[5] - 4[239]
Lehmer's measure1.85112
References
Jones, William. Synopsis palmariorum matheseos, J. Wale, London, 1706. [On page 263, formula is attributed to author's "much esteem'd friend Mr John Machin"]