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An investigation of the comparative efficiency of the different methods inwhich {\pi} is cal- culated. This thesis will compare and contrast fivedifferent methods in calculating {\pi} by first deriving the various proofs toeach method and then creating graphical displays and tables with percentageerrors on each to allow a thorough comparison between each method. It isimportant to realize that usually people refer to {\pi} as 3.142 and use thisshortened value in everyday calculations. However, most people in society donot know that in some of NASAs calculations, must be calculated to 15 decimalplaces (3.141592653589793) for calculations involving the Space StationGuidance Navigation and Control (GNC) code [9]. Furthermore, some people usethe world renown constant everyday yet have no idea where it comes from.  This thesis allows a thorough exploration of the different methods ofcalculating pi by us- ing Mathematica to provide the necessary iterationsneeded and Microsoft excel to plot the various graphs for convergencecomparisons. Finally, the conclusions that have come from this thesisdemonstrate that methods in which oscillations between the positive andnegative region of the line y = {\pi} slow down the rate of convergence and outof the five methods investigated, The infinite series formulated from{\zeta}(8) proves to be one of the fastest infinite series today to convergetowards {\pi}.

The comparative efficiency of the different methods in which Pi is calculated