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Re: symmetry nomenclature

At 11:58 AM 12/19/99 -0800, Leigh Palmer wrote:

One uses cylindrical symmetry for a finite cylinder only as
an approximation, i.e. for rho << distance from nearer end.

Exactly so.

I never remember what "axial symmetry" means. If it is
synonymous with azimuthal symmetry that's fine, but I always
have to ask. It sounds to me like it implies that z is the
ignorable coordinate. That's why I like the term "azimuthal
symmetry" (phi is ignorable). I think it is less ambiguous.

I'm never sure what such things mean, either. There's too much
inconsistent usage. The one that really cracks me up is radial tires. The
key patented component runs in a direction that I cannot bring myself to
call radial. See
http://www.michelin.com/us/eng/groupe/images/ph113g-a.jpg

If you really want to do it right, crystallographers and other permutation
groupies have a sophisticated system for describing symmetries. The piece
of cylinder described above has what I believe is
C_infinity_v
symmetry. Check out
http://newton.ex.ac.uk/people/goss/symmetry/Stereographs.html