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Re: how fill PolarPlot?

Murray Eisenberg wrote:
> I Mathematica 6 I have a PolarPlot, e.g., a 4-leaved rose:
>    PolarPlot[Cos[2 theta], {theta, 0, 2 Pi}]
> How can I fill the inside -- or, what I really want, just the leaf in 
> the right half-plane -- with some color?
> I note that Filling does not seem to be an option for PolarPlot (or for 
> what would be almost as good, ParametricPlot).
> I tried including the following (obtained by converting from :
>    Prolog->RegionPlot[(x^2 + y^2)^(3/2) <= x^2-y^2, {x,-0.02,1},{y,-1,1},
>        Frame->False, AspectRatio->Automatic]
> However, that led to a mysterious error message:
>    $Aborted is not a Graphics primitive or directive.

I got the even more mysterious error "Graphics is not a Graphics 
primitive or directive".

> (Perhaps because of an incompatibility of a Prolog with cartesian 
> coordinates inside a polar coordinate plot??)

Don't know, but in any case the following works.

Show[PolarPlot[Cos[2 theta], {theta, 0, 2 Pi}],
  RegionPlot[(x^2 + y^2)^(3/2) <= x^2 - y^2, {x, -0.02, 1}, {y, -1, 1},
    Frame -> False, AspectRatio -> Automatic]]

Helen Read
University of Vermont

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