DescrizzionExpIPi.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).
Data	5 Magg 2008
Sorgent	Opera propia  Questo diagramma in GIF grafica è stato creato con Mathematica da n.
Autor	Sbyrnes321

Mi, titolar del dirit d'autor per questa opera chì, la meti foeura in del domini publich. Questa norma chì la var in tut el mond. In d'un quai paes chesschì el podarìss vesser minga permetud de la lensg. In del cas: Mi sicuri a chissessia el dirit de drovà quell lavorà chì per qualsessia fin, sota nissuna condizzion, condamench ch'a ghe sìen di condizzion imposte de la lensg.

(* Source code written in Mathematica 6.0, by Steve Byrnes, 2008. I release this code into the public domain. *)

plot1 = Table[
  ListPlot[Table[{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 = " <> ToString[n], 
   AspectRatio -> Automatic], {n, {1, 2, 3, 4, 5, 10, 20, 50, 100}}];

Export["ExpIPi.gif", plot1, "DisplayDurations" -> {2}, 
 "AnimationRepititions" -> Infinity ]