What symmetry will you find in a surface that has an equation of the form $\displaystyle \rho=f(\phi)$ in spherical coordinates? Please explain.

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- Apr 12th 2009, 06:04 PMlogitechSymmetry
What symmetry will you find in a surface that has an equation of the form $\displaystyle \rho=f(\phi)$ in spherical coordinates? Please explain.

- May 23rd 2009, 06:54 PMMedia_ManIt's a visual
Answer: RADIAL symmetry. Notice that $\displaystyle \rho$ represents the "radius" at that point on the 3D figure, and $\displaystyle \phi$ represents the angle off the "north pole" and nowhere in the function is $\displaystyle \theta$ mentioned. Therefore, the function will have the same value regardless of $\displaystyle \theta$, so you can rotate it about the z-axis without changing it's shape, therefore, you have radial symmetry.