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Re: how fill PolarPlot?

Many thanks to all who replied, showing a variety of methods to 
accomplish what I wanted.  Very instructive!

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

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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