File:ExpIPi.gif
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ExpIPi.gif (360 × 323 pixels, file size: 11 KB, MIME type: image/gif, looped, 9 frames, 4.5 s)
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[edit]DescriptionExpIPi.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). |
Date | |
Source |
Own work This diagram was created with Mathematica by n. |
Author | Sbyrnes321 |
Licensing
[edit]Public domainPublic domainfalsefalse |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
(* 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 ]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 19:46, 25 March 2010 | 360 × 323 (11 KB) | Aiyizo (talk | contribs) | optimized animation, converted to 16 color mode | |
17:19, 5 May 2008 | 360 × 323 (20 KB) | Sbyrnes321 (talk | contribs) | {{Information |Description=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 | ||
16:58, 5 May 2008 | 360 × 308 (18 KB) | Sbyrnes321 (talk | contribs) | {{Information |Description=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 |
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