描述EulerFormulaAsLimit.gif	English: This is a demonstration of Euler's formula, exp(i*pi/3) = cos(pi/3) + i*sin(pi/3). 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 the point on the unit circle of the complex plane (dashed line) at angle pi/3 radians from +1. Variant of File:ExpIPi.gif.
日期	2012年1月22日
來源	自己的作品   本GIF 點陣圖使用Mathematica創作。
作者	Sbyrnes321

(* Source code written in Mathematica 6.0, by Steve Byrnes, 2012. I release this code into the public domain. *)

frameticks = {-.25, 0, .25, .5, .75, 1, 1.25};
plot1 = Table[
  Show[ListPlot[
    Table[{Re[(1 + I*Pi/(3 n))^m], Im[(1 + I*Pi/(3 n))^m]}, {m, 0, n}],
    Joined -> True, PlotMarkers -> Automatic, 
    PlotRange -> {{-.3, 1.1}, {-.3, 1.1}}, AxesOrigin -> {0, 0}, 
    Frame -> True, FrameLabel -> {"Real part", "Imaginary part"}, 
    FrameTicks -> {{frameticks, None}, {frameticks, None}}, 
    Frame -> True, PlotLabel -> "n = " <> ToString[n], 
    LabelStyle -> Medium, AspectRatio -> Automatic], 
   ParametricPlot[{Sin[t], Cos[t]}, {t, 0, 2*Pi}, 
    PlotStyle -> Directive[Gray, Dashed]]],
  {n, {1, 2, 3, 4, 5, 10, 20, 50, 100}}];
SetDirectory["C:\\Users\\Steve\\Desktop"];
Export["test.gif", plot1, "DisplayDurations" -> {2}, "AnimationRepititions" -> Infinity, ImageSize -> 200];

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