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Get a ParametricPlot with interactive parameter, to trace the coordinates?

Posted 5 months ago
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I have noticed that by using the Free-form input for parametric plots, clicking the plus icon in the upper right-hand corner displays additional results provided by Wolfram|Alpha. One of which is a slider for the parameter which I am using to create the plot.

For example:

enter image description here
Clicking on the plus sign, I can see the plot, with a text balloon saying:

this subpod is selected. Press shift-enter to request this subpod form Wolfram|Alpha.

Doing what it says I get on a new line in my notebook the parametric plot with an option to trace the curve, somewhat like Manipulate does.

My question is: How can I create such a plot with Mathematica input, not using the free-form?

3 Replies

ParametricPlot[{Cos[t], Sin[2 t]}, {t, 0, 2 Pi}]

DynamicModule[{tr = 1},
 Column[{
   Show[
    ParametricPlot[
     {Cos[t], Sin[2 t ]}, {t, 0, 2 Pi}, 
     GridLines -> 
      Dynamic[List /@ CurrentValue[{"MousePosition", "Graphics"}]]
     , PlotStyle -> Directive[Thin, Gray]
     ],
    Graphics@{Dynamic[First@ParametricPlot[
          {Cos[t], Sin[2 t ]}, {t, 0.0001, 2 Pi tr},
          PlotStyle -> Thick
          ] /. Line -> Arrow]
      }
    , ImageSize -> Large],
   Slider@Dynamic@tr
   }]
 ]
Posted 5 months ago

Thanks. That's what I was looking for.

But, is there any way to extract out this command you wrote of the Wolfram|Alpha subpod?

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