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Re: Getting started with 3D cardioid

  • To: mathgroup at smc.vnet.net
  • Subject: [mg111991] Re: Getting started with 3D cardioid
  • From: Helen Read <hpr at together.net>
  • Date: Mon, 23 Aug 2010 02:40:22 -0400 (EDT)
  • References: <i4r4ab$jt2$1@smc.vnet.net>
  • Reply-to: HPR <read at math.uvm.edu>

On 8/22/2010 8:14 AM, David Thomson wrote:
> I'm new to Mathematica, sorry.  I would like to draw a cardioid
> rotated about its polar axis.  I checked the Mathematica wiki and it
> did not cover this topic (that I could find).  Can someone help me to
> understand how to do this in Mathematica?

The thing to do is represent the cardioid parametrically.

For example, if you start with this cardioid:

r[t_] = 1 - Cos[t]

PolarPlot[r[t], {t, 0, 2 \[Pi]}]

Then express the polar curve parametrically, like so.

x[t_] = r[t] Cos[t];
y[t_] = r[t] Sin[t];

Note that due to symmetry, you need only revolve the top half (t from 0 
to Pi) around the polar axis.

RevolutionPlot3D[{x[t], y[t]}, {t, 0, \[Pi]}, RevolutionAxis -> x]



-- 
Helen Read
University of Vermont


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