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Solids of Revolution

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  • Russ and Lisa
    Has anyone tried to graph the classic surface of Revolution problems from Calculus using GC? It seems like one should be able to see the region in the x-y
    Message 1 of 4 , Oct 3, 2005
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      Has anyone tried to graph the classic surface of Revolution problems from Calculus using
      GC? It seems like one should be able to see the region in the x-y plane, and animate the
      revolution to see the solid of revolution.

      I can see the region by graphing:

      x=(0 if y<((f(x) if y > g(x)) if a<x<b)

      But I can't seem to get the revolution working. Any help would be appreciated.

      Russ
    • Chris Young
      ... I m not sure exactly what the equation your graphing here is. I got a general formula for parameterized curves out of the book Modern Differential
      Message 2 of 4 , Oct 5, 2005
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        On Oct 3, 2005, at 12:45 PM, Russ and Lisa wrote:

        > Has anyone tried to graph the classic surface of Revolution problems
        > from Calculus using GC? It seems like one should be able to see the
        > region in the x-y plane, and animate the revolution to see the solid
        > of revolution.
        >
        > I can see the region by graphing:
        >
        > x=(0 if y<((f(x) if y > g(x)) if a<x<b)
        >
        > But I can't seem to get the revolution working. Any help would be
        > appreciated.
        >
        > Russ

        I'm not sure exactly what the equation your graphing here is. I got a
        general formula for parameterized curves out of the book "Modern
        Differential Geometry of Curves and Surfaces with Mathematica", 2nd ed.
        Boca Raton, FL: CRC Press, by Alfred Gray, on page 457. It's in the
        following attached file, which I also uploaded to the Files section (
        http://groups.yahoo.com/group/GraphingCalcUsers/files/ ) at Files >
        Calculus, Analysis > Surfaces of revolution.
      • Chris Young
        ... Here s an example with a rotating meridian: (Also posted in the Files section at Files Calculus, Analysis Surfaces of revolution.
        Message 3 of 4 , Oct 5, 2005
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          On Oct 3, 2005, at 12:45 PM, Russ and Lisa wrote:

          > Has anyone tried to graph the classic surface of Revolution problems
          > from Calculus using
          > GC? It seems like one should be able to see the region in the x-y
          > plane, and animate the
          > revolution to see the solid of revolution.
          >
          > I can see the region by graphing:
          >
          > x=(0 if y<((f(x) if y > g(x)) if a<x<b)
          >
          > But I can't seem to get the revolution working. Any help would be
          > appreciated.
          >
          > Russ

          Here's an example with a rotating meridian:
        • Chris Young
          ... Maybe the following is more what you wanted. It shows a revolving slice going around inside the surface of revolution. Also uploaded to Files Calculus,
          Message 4 of 4 , Oct 5, 2005
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            On Oct 3, 2005, at 12:45 PM, Russ and Lisa wrote:

            > Has anyone tried to graph the classic surface of Revolution problems
            > from Calculus using
            > GC? It seems like one should be able to see the region in the x-y
            > plane, and animate the
            > revolution to see the solid of revolution.
            >
            > I can see the region by graphing:
            >
            > x=(0 if y<((f(x) if y > g(x)) if a<x<b)
            >
            > But I can't seem to get the revolution working. Any help would be
            > appreciated.
            >
            > Russ

            Maybe the following is more what you wanted. It shows a revolving
            "slice" going around inside the surface of revolution.
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