Keywords: ExpIPi.gif This is a demonstration that Exp i Pi -1 called Euler's formula or Euler's identity It uses the formula 1+z/N N --> Exp z as N increases The Nth power is displayed as a repeated multiplication in the complex plane As N increases you can see that the final result the last point approaches -1 the actual value of Exp i pi Own 2008-05-05 Sbyrnes321 <pre> Source code written in Mathematica 6 0 by Steve Byrnes 2008 I release this code into the public domain plot1 Table ListPlotTable Re 1 + \ImaginaryI \Pi /n m Im 1 + \ImaginaryI \Pi /n m m 0 n PlotJoined -> True PlotMarkers -> Automatic PlotRange -> -2 5 1 1 0 \Pi + 05 AxesOrigin -> 0 0 AxesLabel -> Real part Imaginary part PlotLabel -> N <> ToStringn AspectRatio -> Automatic n 1 2 3 4 5 10 20 50 100 ; Export ExpIPi gif plot1 DisplayDurations -> 2 AnimationRepititions -> Infinity </pre> Animated GIF Images with Mathematica source code |