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Homework Help: Parametric equation

  1. Jun 19, 2014 #1

    Trying to graph this

    I have the traces
    x=y^2 for x>=0 in xy
    Also x=z^3 for z>=0 in xz
    And z=y^(3/2) for y>=0 in yz

    Parametricplot3d in mathematics does nothing to get a picture for this graph and drawing is proofing difficult
    In general what is the best way to plot these when it's not obvious plug in for t?
    Last edited: Jun 19, 2014
  2. jcsd
  3. Jun 19, 2014 #2


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    It's not clear what you are trying to do.

    Is your function f(x,y,z) = (t^2, t^4, t^6) perhaps? Or something else?
  4. Jun 20, 2014 #3
    Yes that is the function of x y z
    I am trying to graph it
  5. Jun 20, 2014 #4


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    I think you mean, vectorially, r(t) = (t^2, t^4, t^6), i.e. x = t^2 etc..
    But from the OP,
    suggests r(t) = (t^6, t^4, t^2).
    It depends what range of t you want to sketch it for.
    It's kind of hard to sketch 3D curves. What exactly have you been asked to do?
  6. Jun 20, 2014 #5
    Sketch the curve
    mathematica doesn't help
    Last edited: Jun 20, 2014
  7. Jun 20, 2014 #6
    The book asks for a sketch I assume there is a reasonable way
    Plot t values?
  8. Jun 20, 2014 #7
    Is this what you are looking for?
    Code (Text):
    ParametricPlot3D[{t^2, t^4, t^6}, {t, 0, 1}]
    If it isn't then perhaps you can explain what is incorrect about that.
  9. Jun 20, 2014 #8
    Is gives a line I am under the impression that the graph is a surface
    What's throwing me off is the book taking the trace in each plane
    Sint,cost,t cylinder along z
  10. Jun 20, 2014 #9

    Ray Vickson

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    No: the point-set you describe is a one-dimensional object = a curve in 3d. If you wanted a surface you would need two independent variables, so you would need to have something like three functions x(u,v), y(u,v), z(u,v) in two variables u and v.
  11. Jun 20, 2014 #10
    In cost,sint,t
    z for all real isn't a cylinder?
  12. Jun 21, 2014 #11

    Code (Text):
    ParametricPlot3D[{Cos[t], Sin[t], t}, {t, 0, 4 Pi}]
    It is perhaps difficult to get a really good 3D view of it, but try from different angles and guess what it is.
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