       ParametricPlot3D vs Reduce

• To: mathgroup at smc.vnet.net
• Subject: [mg124051] ParametricPlot3D vs Reduce
• From: Andrzej Kozlowski <akozlowski at gmail.com>
• Date: Sat, 7 Jan 2012 05:20:10 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```I just came across something somewhat baffling, though it could be the
result of an imperfect understanding of how 3D graphic functions work.
Consider the following three rational functions of two variables, which
we will think of as parameters of a point on a surface in 3D.

rats = {(-b - 2*d - b^3*d^2)/(b*d), (2*b + d + b^4*d +
2*b^3*d^2)/(b^2*d), (-1 - 2*b^3*d - b^2*d^2)/(b^2*d)};

Now, note that:

Reduce[Thread[-1 <= rats <= 1], {b, d}]

False

in other words, there are no values of the parameters b and d for which
the point lies in the unit cube. However:

ParametricPlot3D[rats, {b, -10, 10}, {d, -10, 10},
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
AxesLabel -> {"a", "b", "c"}]

There appear to be several polygons inside the unit cube that should not
be there?

Andrzej Kozlowski

```

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