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 non-over-lapping >triangles will give me "an area". Given 9 perimeter points it is >possible to arrange more than one set of non-over-lapping 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.
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.
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