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Math Help - Symmetry

  1. #1
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    Symmetry

    What symmetry will you find in a surface that has an equation of the form \rho=f(\phi) in spherical coordinates? Please explain.
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  2. #2
    Senior Member
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    It's a visual

    Answer: RADIAL symmetry. Notice that \rho represents the "radius" at that point on the 3D figure, and \phi represents the angle off the "north pole" and nowhere in the function is \theta mentioned. Therefore, the function will have the same value regardless of \theta, so you can rotate it about the z-axis without changing it's shape, therefore, you have radial symmetry.
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