Question

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

Answer 1

Would this be considered a curve or a surface, and why?

Answer 2

the images are the same

Answer 3

I was thinking this would be considered a surface, but I'm not sure how or why I can assert this as a fact.

Answer 4

oh, the picture came out blank?

Answer 5

I try again

Answer 6

:) no worries thnx

Answer 7

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.

Answer 8

@ganeshie8 @freckles @ikram002p @SithsAndGiggles @Zarkon . Please.

Answer 9

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.