Approximation of Pi

Abstract: The inverse tangent function can be used to approximate pi. When approximating pi, the convergence of infinite series or Products are of great importance for the accuracy in the digits in pi. This thesis will present historical Formulas used to approximate pi, especially Gregory-Leibniz and Machin's. Also, the unique Machin two-term formulas will be presented and discussed to show that Machin's way of calculating pi has had great impact on calculating this number.