Okay, somebody let me in on the trick for the resistance across a single
diagonal of the infinite square lattice of say one-ohm resistors. I'd like
both the elegant solution from symmetry which Leigh implied exists, and I'd
like to know the formal Fourier method to go between any pair of junctions --
or at least a sketch of the basic idea behind the latter if it's very
complicated.
I can see that the infinite lattice is symmetric across a diagonal and
hence if I can find the resistance of one of these half planes, I would
just need to need to halve that to get the desired answer. I also remember
the trick for the infinite-in-one-dimension ladder of resistors. But
neither of these ideas seems to help me make much progress on Leigh's
problem.
For that matter, what's the resistance along a single edge rather than a
diagonal? Or what are the resistances for a simple cubic lattice along an
edge, face diagonal, and body diagonal?
Dr. Carl E. Mungan, Assistant Professor http://www.uwf.edu/~cmungan/
Dept. of Physics, University of West Florida, Pensacola, FL 32514-5751
office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu