
Re: Calculating the area of a closed 3D path or ring
Posted:
Mar 13, 2013 12:26 PM


In <513FD11E.93AEB9D8@guy.com>, on 03/12/2013 at 09:06 PM, Math Guy <Math@guy.com> said:
>Looking for some thoughts about how to understand this problem.
There is no such thing as the area of a ring.
>a) if a membrane was stretched across the ring, what would the area >of the membrane be?
A surface with zero variation, but not necessarily with minimal area.
>b) if the ring represented an aperture through which some material >(gas, fluid) must pass, or the flux of some field (electric, etc). >This would be Area B.
I believe that the flux would depend on the physical setup, not just on the ring itself.
>I can imagine that summing the area of individual nonoverlapping >triangles will give me "an area". Given 9 perimeter points it is >possible to arrange more than one set of nonoverlapping triangles, >with each set giving it's own total area  but which one is the >"correct" one if they give different results?
Why would any peicewise linear surface be "correct"? It certainly won't be minimal.
>Comments?
You need to ask a precise question in order to get a precise answer. Define what you mean by the surface associated with the ring and someone may be able to point you to an algorithm for calculating the area.
 Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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