John Machin

John Machin (* 1680 in England, † June 9, 1751 in London) was an astronomer and mathematician with a professorship at Gresham College in London. He is known for his 1706 discovered arctan formula for the circle number

With the help of the Taylor expansion of the arctangent yields a fast converging series for the computation of. This he had used to calculate 100 decimals of. The Leibniz series

Is not suitable for numerical computation because of their slow convergence. An appreciation of this discovery is that it represents the first substantial new method for the numerical calculation of Archimedes. This Archimedean method was still used in 1600 Ludolph van Ceulen for calculation of 35 decimal places. Today, many more arctan formulas of machinscher type are known.