  An investigation of the comparative efficiency of the different methods in
which {\pi} is cal- culated. This thesis will compare and contrast five
different methods in calculating {\pi} by first deriving the various proofs to
each method and then creating graphical displays and tables with percentage
errors on each to allow a thorough comparison between each method. It is
important to realize that usually people refer to {\pi} as 3.142 and use this
shortened value in everyday calculations. However, most people in society do
not know that in some of NASAs calculations, must be calculated to 15 decimal
places (3.141592653589793) for calculations involving the Space Station
Guidance Navigation and Control (GNC) code [9]. Furthermore, some people use
the world renown constant everyday yet have no idea where it comes from.
  This thesis allows a thorough exploration of the different methods of
calculating pi by us- ing Mathematica to provide the necessary iterations
needed and Microsoft excel to plot the various graphs for convergence
comparisons. Finally, the conclusions that have come from this thesis
demonstrate that methods in which oscillations between the positive and
negative region of the line y = {\pi} slow down the rate of convergence and out
of the five methods investigated, The infinite series formulated from
{\zeta}(8) proves to be one of the fastest infinite series today to converge
towards {\pi}.
