       Re: Re: Shade area between two polar curves

• To: mathgroup at smc.vnet.net
• Subject: [mg100194] Re: [mg100172] Re: [mg100154] Shade area between two polar curves
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Thu, 28 May 2009 04:25:44 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <9507429.1243330897252.JavaMail.root@n11> <200905270806.EAA26972@smc.vnet.net>

```The solution below works just fine. In a separate post I offered a
method that uses only PolarPlot. It seems to me that one should not have
to convert to cartesian coordiantes at all in order to do this kind of
filling. The underlying trouble, of course, is that Mathematica does not
currently include a Filling option for PolarPlot or ParametricPlot.

David Park wrote:
> Show[
>  {PolarPlot[{1 + 2 Cos[t], 2}, {t, 0, 2 \[Pi]}],
>   RegionPlot[
>    2 <= Sqrt[x^2 + y^2] <= 1 + 2 x/Sqrt[(x^2 + y^2)], {x, 0,
>     3}, {y, -2, 2},
>    MaxRecursion -> 3,
>    BoundaryStyle -> Thick]},
>  Axes -> False,
>  ImageSize -> 300]
>
> From: Chee Lim Cheung [mailto:CheeLC at sp.edu.sg]
>
> Hi All
>
> I have plotted two graphs using PolarPlot, namely the limacon r=1+2 cos(t)
> and the circle r = 2 from t = 0 to t = 2 Pi. and I wish to shade the area
> inside the limacon but outside the circle. Can anyone suggest a way to do
> it?
>
> Thanks and Regards
> Chee
>
>
>

--
Murray Eisenberg                     murray at math.umass.edu
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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