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Re: a 4d algebraic geometry problem

• To: mathgroup at smc.vnet.net
• Subject: [mg110782] Re: a 4d algebraic geometry problem
• From: Roger Bagula <roger.bagula at gmail.com>
• Date: Mon, 5 Jul 2010 21:15:47 -0400 (EDT)
• References: <i0sal3$epu$1@smc.vnet.net>

I just now got a better rendering:

http://www.flickr.com/photos/fractalmusic/4764898936/
x = Cos[t0]*Sin[p0]; y = Sin[t0]*Sin[p0]; z = Cos[p0];
x1 = Re[Integrate[x^2 + (22/16)*x + 1/3, {p0, 0, t}]];
y1 = Re[Integrate[y^2 + (22/16)*y + 1/3, {p0, 0, t}]];
z1 = Re[Integrate[z^2 + (22/16)*z + 1/3, {p0, 0, t}]];
g1 = ParametricPlot3D[{x1, y1, z1, {
        EdgeForm[]}}, {t, 0, 2*Pi}, {t0, 0, 2*Pi},
        PlotRange -> All, PlotPoints -> {60, 60},
     Boxed -> False, Axes -> False]
g2 = ParametricPlot3D[{x1, y1,
           z1, {EdgeForm[]}}, {t, -2*Pi, 0}, {t0, 0, 2*Pi}, PlotRange -
> All, \
PlotPoints -> {60, 60}, Boxed -> False, Axes -> False]
g3 = ParametricPlot3D[{x1, y1, -z1, {EdgeForm[]}}, {t, 0, 2*Pi}, {t0,
-2*
    Pi, 0}, PlotRange -> All, PlotPoints -> {60, 60}, Boxed ->
      False, Axes -> False]
g4 = ParametricPlot3D[{x1, y1, -
    z1, {EdgeForm[]}}, {t, -2*Pi, 0}, {t0, -2*Pi, 0}, PlotRange ->
All, \
PlotPoints -> {60, 60}, Boxed -> False, Axes -> False]
Show[{g1, g2}, Boxed -> False, Axes -> False]
Show[{g3, g4}, Boxed -> False, Axes -> False]