This is the parametric plot from Clear[x, y, z, r, t, f,surface, threedims]; {x[r_, t_], y[r_, t_], z[r_, t_]} = {1, 0, 1} + {r Cos[t], r Sin[t], 0}; x[r,t] y[r,t] z[r,t] surface = ParametricPlot3D[{x[r, t], y[r, t], z[r, t]}, {r, 0, 2}, {t, 0, 2 Pi}]; threedims = Axes3D[3]; Show[threedims, surface, ViewPoint -> CMView, PlotRange -> All, Boxed -> False] https://drive.google.com/file/d/0B-X-U-ShsowTMUd0X3pybjJaVEU/view?usp=sharing

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This is the parametric plot from Clear[x, y, z, r, t, f,surface, threedims]; {x[r_, t_], y[r_, t_], z[r_, t_]} = {1, 0, 1} + {r Cos[t], r Sin[t], 0}; x[r,t] y[r,t] z[r,t] surface = ParametricPlot3D[{x[r, t], y[r, t], z[r, t]}, {r, 0, 2}, {t, 0, 2 Pi}]; threedims = Axes3D[3]; Show[threedims, surface, ViewPoint -> CMView, PlotRange -> All, Boxed -> False] https://drive.google.com/file/d/0B-X-U-ShsowTMUd0X3pybjJaVEU/view?usp=sharing

Mathematics
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Would this be considered a curve or a surface, and why?
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the images are the same
I was thinking this would be considered a surface, but I'm not sure how or why I can assert this as a fact.

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oh, the picture came out blank?
I try again
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:) no worries thnx
I think maybe the rule is that a curve is a 1 dimensional object in a 2d or 3d space.. I know the circle is 1 dimensional.. And a surface is a 2d object in a 3d space. But I am not sure if a circle within a circle is considered a surface, or if it is just two curves.. or multiple curves.. My guess is that as soon as you add the 2nd circle, it becomes a 2d object.. so being in a 3d space, this becomes a surface.
Considering this is a function of two parameters, I think it qualifies as a surface. Compare to a function like `{x[t_] = Cos[t], y[t_] = Sin[t], z[t_] = t}`, which generates a helix, which is more like a curve or contour.

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