Re: CUBE RESISTANCE

[Chuck Britton <britton@NCSSM.EDU>]

At 7:52 AM -0500 3/4/03, John S. Denker wrote:

>  > bc who simplifies by shorting vertices that have the same potential
>
>   They don't assign it in electrical engineering class,
> because cubical resistor networks have no engineering
> significance.

       The EE profs at major Liberal Arts Universities are quite
familiar with such problem and use them to goad the better students.

> To repeat:  this problem has got nothing to do
> with electronics.  It has everything to do with
> symmetry.

       NOTHING to do with electronics?
       I am AMAZED that JSD doesn't know
       how to build a circuit that uses a common OpAmp  ;-)

       Or MAYBE JSD was just exercising a bit of hyperbole.

       Symmetry, yes. But don't minimize Bernie's "Virtual" connection idea.
       OpAmp users make use of the 'virtual ground' abstraction every day.

> So here is how I would answer the original problem:
>   -- Electrodes at the corners are "special" points.
>   -- Threefold symmetry about the special points.
>   -- Do the sub-problem:  R + two Rs in parallel + R
>   -- Three copies of the subproblem makes 2.5 thirds.

       I would specifically add the virtual connections redraw the
twelve R's. Put the first three R's in parallel, + six R's in
parallel + the final three R's in parallel.