Continuous Symmetries
The two examples of rotational symmetry described above - spherical and cylindrical - are each instances of continuous symmetry. These are characterised by invariance following a continuous change in the geometry of the system. For example, the wire may be rotated through any angle about its axis and the field strength will be the same on a given cylinder. Mathematically, continuous symmetries are described by continuous or smooth functions. An important subclass of continuous symmetries in physics are spacetime symmetries.
Read more about this topic: Symmetry (physics)
Famous quotes containing the word continuous:
“The habit of common and continuous speech is a symptom of mental deficiency. It proceeds from not knowing what is going on in other people’s minds.”
—Walter Bagehot (1826–1877)