what is azimuthal symmetry
Consider yourself faceing North on a plane. Going East, full circle, imagine a pole each 20 degrees. As you turn, you see the poles each 20 degrees of turn. The poles have azimuthal symettry. Now imagine each third pole is twice as high..again, symettry in the azmiuth.
Many things have azimuthal symettry. On my ship driving days, the compass rose comes to mind.
http://www.enchantedlearning.com/geography/printouts/compassrose.shtml
Azimuthal symmetry refers to a type of symmetry that occurs in a circular object when it looks the same from all angles around a central point. In other words, if you were to rotate the object around its central axis, it would maintain its overall shape and appearance.
To understand azimuthal symmetry, you can think of a compass rose as an example. A compass rose is a diagram used on maps to indicate the orientation of North, South, East, and West. It typically consists of lines or arrows radiating from a central point. If you imagine yourself facing North on a plane and rotate around in a full circle, you will see that the compass rose looks the same from every angle. Each line or arrow remains at the same angle and distance relative to the others, maintaining its overall symmetry. This is an example of azimuthal symmetry.
You can explore more about azimuthal symmetry in various objects and designs by observing their shapes and patterns. By rotating them around their central axis, you can determine if they possess azimuthal symmetry.