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| View Original: | EulerFormulaAsLimit.gif (200x204) | |||
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| Keywords: EulerFormulaAsLimit.gif en 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 2012-01-22 own Sbyrnes321 <pre> 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 ShowListPlot 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 <> ToStringn LabelStyle -> Medium AspectRatio -> Automatic ParametricPlot Sint Cost t 0 2 Pi PlotStyle -> DirectiveGray 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; </pre> cc-zero Uploaded with UploadWizard Images with Mathematica source code Animated GIF | ||||
