M000000223

$$\pi=32\arctan\left(\frac{1}{10}\right)-4\arctan\left(\frac{1}{239}\right)-16\arctan\left(\frac{1}{515}\right)$$
Compact formula32[10] - 4[239] - 16[515]
Lehmer's measure1.78920
References
Simson, Robert. Paper on series, enclosed in a letter to James Jurin, 1723. [Printed in "Account of the life and writings of Robert Simson, M.D., late professor of mathematics in the University of Glasgow" (pages 105–111) by Trail, William, 1812.]