# Symmetry

Printable View

• Apr 12th 2009, 07:04 PM
logitech
Symmetry
What symmetry will you find in a surface that has an equation of the form $\rho=f(\phi)$ in spherical coordinates? Please explain.
• May 23rd 2009, 07:54 PM
Media_Man
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.