# How do you put a dynamic in the limit of ParametricPlot without plln error?

Posted 10 years ago
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 I can run the following code without issue:DynamicModule[{\[Alpha] = {1, 0}}, {Show[   Graphics[{{Dashed, Circle[], PointSize[0.1]},      Locator[Dynamic[\[Alpha], (\[Alpha] = Normalize[#]) &]]},     ImageSize -> Medium, PlotRange -> 1.2],    ParametricPlot[{r*Cos[t], r*Sin[t]}, {r, 0,      Sqrt[(1 - 0.25)/2]}, {t, 0, 2*\[Pi]}, PlotStyle -> {Red}]]}]But when I introduce a dynamic to the upper limit of the radius r of the red disc using:DynamicModule[{\[Alpha] = {1, 0}}, {Show[   Graphics[{{Dashed, Circle[], PointSize[0.1]},      Locator[Dynamic[\[Alpha], (\[Alpha] = Normalize[#]) &]]},     ImageSize -> Medium, PlotRange -> 1.2],    ParametricPlot[{r*Cos[t], r*Sin[t]}, {r, 0,      Sqrt[(1 - Dynamic[\[Alpha][[1]]])/2]}, {t, 0, 2*\[Pi]},     PlotStyle -> {Red}]]}]I get the error:ParametricPlot::plln: "Limiting value \!$$\*FractionBox[SqrtBox[RowBox[{\"1\", \"-\", DynamicBox[ToBoxes[Part[\38748, 1], StandardForm],ImageSizeCache->{7., {0., 8.}}]}]], SqrtBox[\"2\"]]$$ in \!$${r, 0, \*SqrtBox[FractionBox[RowBox[{\"1\", \"-\", DynamicBox[ToBoxes[Part[\38748, 1], StandardForm],ImageSizeCache->{7., {0., 8.}}]}], \"2\"]]}$$ is not a machine-sized real number. "What is going on here? Can anyone help me sort out a dynamic as a limit in a Parametric Plot without plln error?Any help much appreciated. Thanks.