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Re: Getting started with 3D cardioid

• To: mathgroup at smc.vnet.net
• Subject: [mg112073] Re: Getting started with 3D cardioid
• From: David Thomson <aetherwizard at gmail.com>
• Date: Sun, 29 Aug 2010 02:49:24 -0400 (EDT)
• References: <i57rp6$1in$1@smc.vnet.net>

On Aug 27, 3:08 am, Alexei Boulbitch <alexei.boulbi... at iee.lu> wrote:
> Hi, David,
>
> To answer your first question:
> I do not understand, where the figure 68 for the average radius comes
> from?

The number is not 68, but decimal point 68.  ie ".68".

> Concerning your second question:
>
> I am not aware of the horn shape and it would be helpful, if you  post
> the  corresponding formula in whatever coordinates.

My ignorance is to blame for providing incomplete information.  The
shape I am trying to model is here"
http://www.secrets-of-the-aether.com/images/stories/idealtcshape-damped_wave.jpg

This shape comes from:
r[t_] = Sin[t + 1]/t
PolarPlot[r[t], {t, 0, \[Pi]}]

By trial and error, I got the graph about where it should be:

r[t_] = Sin[t + 1]/t^2;
x[t_] = r[t] Cos[t];
y[t_] = r[t] Sin[t];
RevolutionPlot3D[{x[t + 1], y[t - \[Pi]]}, {t, 0, 1},
 RevolutionAxis -> x]

I tried the Show function to merge the above graph with the cardioid
graph, but got error messages.  How do I merge the SphericalPlot3D
image with the RevolutionPlot3D image?

Thanks,

Dave