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How would I plot $x^2+y^2=1$ in 3D (it would form a cylinder)? Since there is no $z$ in the equation, I can't solve for it and use Plot3D. Or can I just put the equation into Plot3D? I am very new to Mathematica.

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2 Answers

up vote 11 down vote accepted

How about a 3D contour plot.

ContourPlot3D[x^2 + y^2 == 1, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}]
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Oh, great! Thanks! – Ben7005 Sep 16 '12 at 22:52
No problem! Have fun Ben. – Mark McClure Sep 16 '12 at 22:54
up vote 9 down vote

Although Mark's answer is the "natural" one, here are other options just for completeness:

Use Plot3D, after performing a rotation:

Plot3D[{1, -1} Sqrt[1 - x x], {x, -1, 1}, {y, -1, 1},  AspectRatio -> 1]

Mathematica graphics

Use ParametricPlot3D[]:

ParametricPlot3D[{{1, -1, 1} #, {1, 1, 1} #} &@{x, Sqrt[1 - x x], z}, {x, -1, 1}, {z, 0, 1}]

Mathematica graphics

Use RevolutionPlot3D[] after realizing for example that in the semi/plane {y==0, x>0} x takes only the value 1 and z takes any value (freely):

RevolutionPlot3D[{1, t}, {t, 0, 1}]

Mathematica graphics

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Yet another possibility: ParametricPlot3D[RotationTransform[θ, {0, 0, 1}][{1, 0, r}] // Evaluate, {r, 0, 1}, {θ, 0, 2 π}] – 0x4A4D♦ Sep 17 '12 at 11:00
Man, thanks so much for this. This is great. – Ben7005 Sep 19 '12 at 2:00

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